• Anderson, D. M., , B. A. Keafer, , W. R. Geyer, , R. P. Signell, , and T. C. Loder, 2005: Toxic Alexandrium blooms in the western Gulf of Maine: the plume advection hypothesis revisited. Limnol. Oceanogr., 50 , 328345.

    • Search Google Scholar
    • Export Citation
  • Barnes, C. A., , A. C. Duxbury, , and B. A. Morse, 1972: Circulation and selected properties of the Columbia River effluent at sea. The Columbia River Estuary and Adjacent Ocean Waters, A. T. Pruter and D. L. Alverson, Eds., University of Washington Press, 41–80.

    • Search Google Scholar
    • Export Citation
  • Barron, C. N., , A. B. Kara, , P. J. Martin, , R. C. Rhodes, , and L. F. Smedstad, 2006: Formulation, implementation and examination of vertical coordinate choices in the Global Navy Coastal Ocean Model (NCOM). Ocean Modell., 11 , 347375. doi:10.1016/j.ocemod.2005.01.004.

    • Search Google Scholar
    • Export Citation
  • Battisti, D. S., , and B. M. Hickey, 1984: Application of remote wind-forced coastal trapped wave theory to the Oregon and Washington coasts. J. Phys. Oceanogr., 14 , 887903.

    • Search Google Scholar
    • Export Citation
  • Canuto, V. M., , A. Howard, , Y. Cheng, , and M. S. Dubovikov, 2001: Ocean turbulence. Part I: One-point closure model—Momentum and heat vertical diffusivities. J. Phys. Oceanogr., 31 , 14131426.

    • Search Google Scholar
    • Export Citation
  • Chant, R. J., , S. M. Glenn, , E. Hunter, , J. Kohut, , R. F. Chen, , R. W. Houghton, , J. Bosch, , and O. Schofield, 2008: Bulge formation of a buoyant river outflow. J. Geophys. Res., 113 , C01017. doi:10.1029/2007JC004100.

    • Search Google Scholar
    • Export Citation
  • Chao, S-Y., , and W. C. Boicourt, 1986: Onset of estuarine plumes. J. Phys. Oceanogr., 16 , 21372149.

  • Chapman, D. C., 1985: Numerical treatment of cross-shelf open boundaries in a barotropic coastal ocean model. J. Phys. Oceanogr., 15 , 10601075.

    • Search Google Scholar
    • Export Citation
  • Chen, F., , and D. G. MacDonald, 2006: Role of mixing in the structure and evolution of a buoyant discharge plume. J. Geophys. Res., 111 , C11002. doi:10.1029/2006JC003563.

    • Search Google Scholar
    • Export Citation
  • Choi, B., , and J. L. Wilkin, 2007: The effect of wind on the dispersal of the Hudson River Plume. J. Phys. Oceanogr., 37 , 18781897.

  • Davis, R. E., 1985: Drifter observations of coastal surface currents during CODE: The method and descriptive view. J. Geophys. Res., 90 , (C3). 47414755.

    • Search Google Scholar
    • Export Citation
  • Divins, D. L., , and D. Metzger, cited. 2002: NGDC/MGG-Coastal Relief Model. [Available online at http://www.ngdc.noaa.gov/mgg/coastal/crm.html].

    • Search Google Scholar
    • Export Citation
  • Dong, C., , J. C. McWilliams, , and A. F. Shchepetkin, 2007: Island wakes in deep water. J. Phys. Oceanogr., 37 , 962981.

  • Egbert, G. D., , and S. Y. Erofeeva, 2002: Efficient inverse modeling of barotropic ocean tides. J. Atmos. Oceanic Technol., 19 , 183204.

    • Search Google Scholar
    • Export Citation
  • Egbert, G. D., , A. Bennett, , and M. Foreman, 1994: TOPEX/Poseidon tides estimated using a global inverse model. J. Geophys. Res., 99 , (C12). 2482124852.

    • Search Google Scholar
    • Export Citation
  • Fairall, C. W., , E. F. Bradley, , J. S. Godfrey, , G. A. Wick, , J. B. Edson, , and G. S. Young, 1996a: Cool-skin and warm-layer effects on sea surface temperature. J. Geophys. Res., 101 , (C1). 12951308.

    • Search Google Scholar
    • Export Citation
  • Fairall, C. W., , E. F. Bradley, , D. P. Rogers, , J. B. Edson, , and G. S. Young, 1996b: Bulk parameterization of air-sea fluxes for Tropical Ocean-Global Atmosphere Coupled-Ocean Atmosphere Response Experiment. J. Geophys. Res., 101 , (C2). 37473764.

    • Search Google Scholar
    • Export Citation
  • Flather, R. A., 1976: A tidal model of the northwest European continental shelf. Mem. Soc. Roy. Sci. Liege, 6 , 141164.

  • Fong, D. A., , and W. R. Geyer, 2001: Response of a river plume during an upwelling favorable wind event. J. Geophys. Res., 106 , (C1). 10671084.

    • Search Google Scholar
    • Export Citation
  • Fong, D. A., , and W. R. Geyer, 2002: The alongshore transport of freshwater in a surface-trapped river plume. J. Phys. Oceanogr., 32 , 957972.

    • Search Google Scholar
    • Export Citation
  • Fong, D. A., , W. R. Geyer, , and R. P. Signell, 1997: The wind-forced response on a buoyant coastal current: Observations of the western Gulf of Maine plume. J. Mar. Syst., 12 , 6981.

    • Search Google Scholar
    • Export Citation
  • García Berdeal, I., , B. M. Hickey, , and M. Kawase, 2002: Influence of wind stress and ambient flow on a high discharge river plume. J. Geophys. Res., 107 , 3130. doi:10.1029/2001JC000932.

    • Search Google Scholar
    • Export Citation
  • Geyer, W. R., , J. H. Trowbridge, , and M. M. Bowen, 2000: The dynamics of a partially mixed estuary. J. Phys. Oceanogr., 30 , 20352048.

  • Haidvogel, D. B., , H. G. Arango, , K. Hedstrom, , A. Beckmann, , P. Malanotte-Rizzoli, , and A. F. Shchepetkin, 2000: Model evaluation experiments in the North Atlantic Basin: Simulations in nonlinear terrain-following coordinates. Dyn. Atmos. Oceans, 32 , 239281.

    • Search Google Scholar
    • Export Citation
  • Hearn, C. J., , J. R. Hunter, , J. Imberger, , and D. van Senden, 1985: Tidally induced jet in Koombana Bay, Western Australia. Aust. J. Mar. Freshwater Res., 36 , 453479.

    • Search Google Scholar
    • Export Citation
  • Hench, J. L., , and R. A. Luettich Jr., 2003: Transient tidal circulation and momentum balances at a shallow inlet. J. Phys. Oceanogr., 33 , 913932.

    • Search Google Scholar
    • Export Citation
  • Hetland, R. D., 2005: Relating river plume structure to vertical mixing. J. Phys. Oceanogr., 35 , 16671688.

  • Hetland, R. D., , and D. G. MacDonald, 2008: Spreading in the near-field Merrimack River plume. Ocean Modell., 21 , 1221. doi:10.1016/j.ocemod.2007.11.001.

    • Search Google Scholar
    • Export Citation
  • Hickey, B. M., 1989: Patterns and processes of circulation over the Washington continental shelf and slope. Coastal Oceanography of Washington and Oregon, M. R. Landry and B. M. Hickey, Eds., Elsevier, 41–115.

    • Search Google Scholar
    • Export Citation
  • Hickey, B. M., , L. J. Pietrafesa, , D. A. Jay, , and W. C. Boicourt, 1998: The Columbia River Plume Study: Subtidal variability in the velocity and salinity fields. J. Geophys. Res., 103 , (C5). 1033910368.

    • Search Google Scholar
    • Export Citation
  • Hickey, B. M., , S. Geier, , N. Kachel, , and A. MacFadyen, 2005: A bi-directional river plume: The Columbia in summer. Cont. Shelf Res., 25 , 16311656. doi:10.1016/j.csr.2005.04.010.

    • Search Google Scholar
    • Export Citation
  • Hickey, B. M., , R. McCabe, , S. Geier, , E. Dever, , and N. Kachel, 2009: Three interacting freshwater plumes in the northern California Current System. J. Geophys. Res., 114 , C00B03. doi:10.1029/2008JC004907.

    • Search Google Scholar
    • Export Citation
  • Holton, J. R., 1992: An Introduction to Dynamic Meteorology. 3rd ed. Academic Press, 511 pp.

  • Horner-Devine, A. R., 2009: The bulge circulation in the Columbia River plume. Cont. Shelf Res., 29 , 234251. doi:10.1016/j.csr.2007.12.012.

    • Search Google Scholar
    • Export Citation
  • Horner-Devine, A. R., , D. A. Fong, , S. G. Monismith, , and T. Maxworthy, 2006: Laboratory experiments simulating a coastal river inflow. J. Fluid Mech., 555 , 203232. doi:10.1017/S0022112006008937.

    • Search Google Scholar
    • Export Citation
  • Horner-Devine, A. R., , D. A. Jay, , P. M. Orton, , and E. Y. Spahn, 2009: A conceptual model of the strongly tidal Columbia River plume. J. Mar. Syst., 78 , 460475. doi:10.1016/j.jmarsys.2008.11.025.

    • Search Google Scholar
    • Export Citation
  • Kara, A. B., , C. N. Barron, , P. J. Martin, , L. F. Smedstad, , and R. C. Rhodes, 2006: Validation of interannual simulations from the 1/8° global Navy Coastal Ocean Model (NCOM). Ocean Modell., 11 , 376398. doi:10.1016/j.ocemod.2005.01.003.

    • Search Google Scholar
    • Export Citation
  • Kashiwamura, M., , and S. Yoshida, 1967: Outflow pattern of fresh water issued from a river mouth. Coastal Eng. J., 10 , 109115.

  • Lentz, S. J., 2004: The response of buoyant coastal plumes to upwelling-favorable winds. J. Phys. Oceanogr., 34 , 24582469.

  • Li, M., , L. Zhong, , and W. C. Boicourt, 2005: Simulations of Chesapeake Bay estuary: Sensitivity to turbulence mixing parameterizations and comparison with observations. J. Geophys. Res., 110 , C12004. doi:10.1029/2004JC002585.

    • Search Google Scholar
    • Export Citation
  • Liu, W. T., , K. B. Katsaros, , and J. A. Businger, 1979: Bulk parameterization of air-sea exchanges of heat and water vapor including the molecular constraints at the interface. J. Atmos. Sci., 36 , 17221735.

    • Search Google Scholar
    • Export Citation
  • Liu, Y., , P. MacCready, , and B. M. Hickey, 2009a: Columbia River plume patterns in summer 2004 as revealed by a hindcast coastal ocean circulation model. Geophys. Res. Lett., 36 , L02601. doi:10.1029/2008GL036447.

    • Search Google Scholar
    • Export Citation
  • Liu, Y., , P. MacCready, , B. M. Hickey, , E. P. Dever, , P. M. Kosro, , and N. S. Banas, 2009b: Evaluation of a coastal ocean circulation model for the Columbia River plume in summer 2004. J. Geophys. Res., 114 , C00B04. doi:10.1029/2008JC004929.

    • Search Google Scholar
    • Export Citation
  • Lohan, M. C., , and K. W. Bruland, 2006: Importance of vertical mixing for additional sources of nitrate and iron to surface waters of the Columbia River plume: Implications for biology. Mar. Chem., 98 , 260273. doi:10.1016/j.marchem.2005.10.003.

    • Search Google Scholar
    • Export Citation
  • Luketina, D. A., , and J. Imberger, 1987: Characteristics of a surface buoyant jet. J. Geophys. Res., 92 , (C5). 54355447.

  • Luketina, D. A., , and J. Imberger, 1989: Turbulence and entrainment in a buoyant surface plume. J. Geophys. Res., 94 , (C9). 1261912636.

    • Search Google Scholar
    • Export Citation
  • MacCready, P., , N. S. Banas, , B. M. Hickey, , E. P. Dever, , and Y. Liu, 2009: A model study of tide- and wind-induced mixing in the Columbia River estuary and plume. Cont. Shelf Res., 29 , 278291. doi:10.1016/j.csr.2008.03.015.

    • Search Google Scholar
    • Export Citation
  • MacDonald, D. G., , and W. R. Geyer, 2004: Turbulent energy production and entrainment at a highly stratified estuarine front. J. Geophys. Res., 109 , C05004. doi:10.1029/2003JC002094.

    • Search Google Scholar
    • Export Citation
  • MacDonald, D. G., , and W. R. Geyer, 2005: Hydraulic control of a highly stratified estuarine front. J. Phys. Oceanogr., 35 , 374387.

  • MacDonald, D. G., , L. Goodman, , and R. D. Hetland, 2007: Turbulent dissipation in a near-field river plume: A comparison of control volume and microstructure observations with a numerical model. J. Geophys. Res., 112 , C07026. doi:10.1029/2006JC004075.

    • Search Google Scholar
    • Export Citation
  • Marchesiello, P., , J. C. McWilliams, , and A. Shchepetkin, 2001: Open boundary conditions for long-term integration of regional oceanic models. Ocean Modell., 3 , 120.

    • Search Google Scholar
    • Export Citation
  • Marchesiello, P., , J. C. McWilliams, , and A. Shchepetkin, 2003: Equilibrium structure and dynamics of the California Current system. J. Phys. Oceanogr., 33 , 753783.

    • Search Google Scholar
    • Export Citation
  • Mass, C. F., and Coauthors, 2003: Regional environmental prediction over the Pacific Northwest. Bull. Amer. Meteor. Soc., 84 , 13531366.

    • Search Google Scholar
    • Export Citation
  • Masse, A. K., , and C. R. Murthy, 1990: Observations of the Niagara River thermal plume (Lake Ontario, North America). J. Geophys. Res., 95 , (C9). 1609716109.

    • Search Google Scholar
    • Export Citation
  • McCabe, R. M., , B. M. Hickey, , and P. MacCready, 2008: Observational estimates of entrainment and vertical salt flux in the interior of a spreading river plume. J. Geophys. Res., 113 , C08027. doi:10.1029/2007JC004361.

    • Search Google Scholar
    • Export Citation
  • Naik, P. K., , and D. A. Jay, 2005: Estimation of Columbia River virgin flow: 1879 to 1928. Hydrol. Processes, 19 , 18071824. doi:10.1002/hyp.5636.

    • Search Google Scholar
    • Export Citation
  • Nash, J. D., , and J. N. Moum, 2005: River plumes as a source of large-amplitude internal waves in the coastal ocean. Nature, 437 , 400403. doi:10.1038/nature03936.

    • Search Google Scholar
    • Export Citation
  • Nash, J. D., , L. F. Kilcher, , and J. N. Moum, 2009: Structure and composition of a strongly stratified, tidally pulsed river plume. J. Geophys. Res., 114 , C00B12. doi:10.1029/2008JC005036.

    • Search Google Scholar
    • Export Citation
  • O’Donnell, J., , G. O. Marmorino, , and C. L. Trump, 1998: Convergence and downwelling at a river plume front. J. Phys. Oceanogr., 28 , 14811495.

    • Search Google Scholar
    • Export Citation
  • Orton, P. M., , and D. A. Jay, 2005: Observations at the tidal plume front of a high-volume river outflow. Geophys. Res. Lett., 32 , L11605. doi:10.1029/2005GL022372.

    • Search Google Scholar
    • Export Citation
  • Sanders, T. M., , and R. W. Garvine, 2001: Fresh water delivery to the continental shelf and subsequent mixing: An observational study. J. Geophys. Res., 106 , (C11). 2708727101.

    • Search Google Scholar
    • Export Citation
  • Shchepetkin, A. F., , and J. C. McWilliams, 2005: The regional oceanic modeling system (ROMS): A split-explicit, free-surface, topography-following-coordinate oceanic model. Ocean Modell., 9 , 347404. doi:10.1016/j.ocemod.2004.08.002.

    • Search Google Scholar
    • Export Citation
  • Shulman, I., , J. C. Kindle, , S. deRada, , S. C. Anderson, , B. Penta, , and P. J. Martin, 2003: Development of a hierarchy of nested models to study the California Current System. Proc. Eighth Int. Conf. on Estuarine and Coastal Modeling, Monterey, CA, Amer. Soc. Civil Eng., 74–88.

    • Search Google Scholar
    • Export Citation
  • Shulman, I., and Coauthors, 2007: Modeling of upwelling/relaxation events with the Navy Coastal Ocean Model. J. Geophys. Res., 112 , C060623. doi:10.1029/2006JC003946.

    • Search Google Scholar
    • Export Citation
  • Tinis, S. W., , R. E. Thomson, , C. F. Mass, , and B. M. Hickey, 2006: Comparison of MM5 and meteorological buoy winds from British Columbia to Northern California. Atmos.–Ocean, 44 , 6581.

    • Search Google Scholar
    • Export Citation
  • Umlauf, L., , and H. Burchard, 2003: A generic length-scale equation for geophysical turbulence models. J. Mar. Res., 61 , 235265.

  • Vennell, R., 2006: ADCP measurements of momentum balance and dynamic topography in a constricted tidal channel. J. Phys. Oceanogr., 36 , 177188.

    • Search Google Scholar
    • Export Citation
  • Warner, J. C., , W. R. Geyer, , and J. A. Lerczak, 2005a: Numerical modeling of an estuary: A comprehensive skill assessment. J. Geophys. Res., 110 , C05001. doi:10.1029/2004JC002691.

    • Search Google Scholar
    • Export Citation
  • Warner, J. C., , C. R. Sherwood, , H. G. Arango, , and R. P. Signell, 2005b: Performance of four turbulence closure models implemented using a generic length scale method. Ocean Modell., 8 , 81113. doi:10.1016/j.ocemod.2003.12.003.

    • Search Google Scholar
    • Export Citation
  • Whitney, M. M., , and R. W. Garvine, 2005: Wind influence on a coastal buoyant outflow. J. Geophys. Res., 110 , C03014. doi:10.1029/2003JC002261.

    • Search Google Scholar
    • Export Citation
  • Wilkin, J. L., , and W. G. Zhang, 2007: Modes of mesoscale sea surface height and temperature variability in the East Australian Current. J. Geophys. Res., 112 , C01013. doi:10.1029/2006JC003590.

    • Search Google Scholar
    • Export Citation
  • Wright, L. D., , and J. M. Coleman, 1971: Effluent expansion and interfacial mixing in the presence of a salt wedge, Mississippi River Delta. J. Geophys. Res., 76 , 86498661.

    • Search Google Scholar
    • Export Citation
  • Yankovsky, A. E., , and D. C. Chapman, 1997: A simple theory for the fate of buoyant coastal discharges. J. Phys. Oceanogr., 27 , 13861401.

    • Search Google Scholar
    • Export Citation
  • Zhang, W. G., , J. L. Wilkin, , and R. J. Chant, 2009: Modeling the pathways and mean dynamics of river plume dispersal in the New York Bight. J. Phys. Oceanogr., 39 , 11671183.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    (left) The entire domain of the numerical model, which includes the Washington and northern Oregon shelf and slope and the Columbia River estuary. The resolution of the stretched grid is shown with tick marks at the edges. The Columbia River channel beyond 50 km from the coast is replaced by a straight channel, which absorbs tidal energy. Bathymetry contour intervals are 100 (thin lines) and 500 m (thick lines). The two bays north of the Columbia River mouth are Willapa Bay and Grays Harbor. (right) A close-up of the gray region in (left). Here, thin lines show isobaths on the shelf at 50-m intervals, and the grid resolution is ∼400 m.

  • View in gallery

    A time series of 9 Jun 2005 tidal conditions at the Columbia River mouth (46.2542°N, 124.0833°W) from the model. Model surface elevation η (m) is represented by the thick black line and model surface currents U (m s−1) are represented by the thick gray line. Negative (positive) currents ebb (flood) out (into) the estuary. Three different times have been chosen to represent the greater ebb: near maximum ebb (before tidal currents significantly relax), midebb, and just after slack conditions.

  • View in gallery

    (a) A comparison between observed surface drifter tracks (four thick gray lines) from an experiment on 9 Jun 2005 (see McCabe et al. 2008) and numerical surface floats (tracks colored by salinity) from a realistic ROMS hindcast. Field drifters were released on a greater ebb, near the time of maximum ebb currents. Model floats pass the field drifter release locations within ∼10 min of the field deployment times. All tracks are 8 h long. Bathymetric contours (thin gray lines) are drawn at 10-, 20-, 50-, 100-, 200-, and 500-m depths. The time series of mean observed and numerical float (b) salinities and (c) speeds show plume dilution and flow deceleration.

  • View in gallery

    Model flow properties (∼30-min average) in the near-field region of the Columbia River plume, near the time of maximum ebb currents. (b),(d)–(o) Surface plan view (lat, lon). (a) Tidal height and surface currents from Fig. 2, showing timing with respect to tidal phase and averaging duration (vertical gray band); (b) a plan view of the surface salinity S with bathymetry contours at 10-, 20-, 50-, 100-, 200-, and 500-m depths in black; (c) a vertical section of salinity (S = 26, drawn black) along the dashed white line in (b); (d) sea surface height anomaly Δη (cm) relative to a nearshore value outside of buoyant plume water, with bathymetry contours as in (b); and (e) surface velocity vectors showing the ebb momentum pulse. Contributions to the surface streamwise momentum balance (m s−2): (f) local acceleration, the first term in Eq. (1); (g) total advective acceleration, which is the sum of the second and third terms in Eq. (1); (h) the streamwise pressure gradient field, which is the fourth term in Eq. (1); (i) Coriolis acceleration, which is zero by definition; and (j) the streamwise vertical stress divergence, which is the sum of the fifth and sixth terms in Eq. (1). Contributors to the surface stream-normal momentum balance (m s−2): (k) rotary acceleration, which is the first term in Eq. (2); (l) stream-normal advective acceleration, which is the sum of the second and third terms in Eq. (2) (primarily centrifugal near the surface); (m) the stream-normal pressure gradient, which is the fifth term in Eq. (2); (n) Coriolis acceleration, which is the fourth term in Eq. (2); and (o) stream-normal vertical stress divergence, which is the sum of the sixth and seventh terms in Eq. (2).

  • View in gallery

    As in Fig. 4, but for midebb. Seven surface float tracks (gray lines) are also shown in all plan-view panels. Black dots mark the current float positions. Floats were released across the river mouth at the time of Fig. 4 (maximum ebb) and have therefore traveled for ∼2.5 h.

  • View in gallery

    As in Fig. 4, but near slack conditions. Seven surface float tracks (gray lines) are also shown in all plan-view panels. Black dots mark the current float positions. Floats were released across the river mouth at the time of Fig. 4 (maximum ebb) and have therefore traveled for ∼4.5 h.

  • View in gallery

    (a) A plan view of the model surface salinity near the time of slack conditions (as in Fig. 6b), including the seven surface float tracks (gray). Current float positions are denoted with black dots. Three float tracks (north, central, and south) are highlighted magenta. Streamwise–normal momentum contributions following the highlighted float tracks are included: (b) north, (c) central, and (d) south. Color-coded momentum equations are also included as a legend for identifying specific momentum terms. The naming convention is consistent with Figs. 4 –6. Temporal derivatives are dotted black lines, advective terms are red lines, pressure gradient terms are green lines, friction terms are blue lines, and the Coriolis accelerations are solid black lines.

  • View in gallery

    Vertical sections of (a) salinity, (b) streamwise vertical shear (s−1) calculated relative to the surface flow direction, (c) stress (10−4 m2 s−2) with surface wind stress appended at the top, and (d) vertical salt flux (10−3 m s−1) through the outflowing plume at midebb (i.e., the time of Fig. 5). The negative values in (c) are in a region of up-estuary flow (to the right). Each section was taken along the transect shown in Fig. 5b and was averaged over ∼31 min. For reference, the isohaline with salinity 26 is drawn as black lines. The largest vertical momentum and salt fluxes in the plume occur at lift-off. However, much also occurs in the plume interior at midplume depths where stratification and vertical shear are large.

  • View in gallery

    Plume spreading as measured with a pair of surface-trapped horizontal Lagrangian drifters. Two adjacent drifters are at positions r1(t) and r2(t) at time t. The drifters have instantaneous velocity vectors U1(t) and U2(t), with local streamline angles α1 and α2. Drifter separation is given by B = r2(t) − r1(t), and the spreading rate following the drifters is dU = U2(t) − U1(t) = DB/Dt.

  • View in gallery

    The distance (km) between adjacent model floats (B; thick black line) in Fig. 7a for the last half of the ebb cycle. Floats were released near the time of maximum ebb currents (at the time of Fig. 4). Also included are the portions of float spreading that result from differences in adjacent float streamwise velocities [BU); thick gray line] and from differences in adjacent float directions [Bα); thin black line].

  • View in gallery

    Cumulative along-track integrals of the Coriolis (thick black line), cross-stream pressure gradient (thick gray line), and cross-stream frictional stress (dashed gray line) terms of the normal-direction momentum equation following numerical floats, and their sum (dashed black line) as a function of time. Floats are selected from the (a) north side, (b) center, and (c) south side of the plume.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 71 71 25
PDF Downloads 74 74 32

Ebb-Tide Dynamics and Spreading of a Large River Plume

View More View Less
  • 1 Department of Aviation, University of New South Wales, Sydney, New South Wales, Australia
  • 2 School of Oceanography, University of Washington, Seattle, Washington
© Get Permissions
Full access

Abstract

Momentum balances in the near-field region of a large, tidally pulsed river plume are examined. The authors concentrate on a single ebb tide of the Columbia River plume, using the Regional Ocean Modeling System (ROMS) configured to hindcast flow conditions on the Washington and Oregon shelves and in the Columbia River estuary. During ebb, plume-interior streamwise balances are largely between advection, pressure gradient, and frictional forces. Stream-normal balances in this region reduce to centrifugal, cross-stream pressure gradient, and Coriolis terms (i.e., the “gradient wind” balance commonly assumed in river plume bulge investigations). Temporal derivatives are most important at the plume front and as the ebb progresses. Winds were light and contributed little to the force balance. Midebb stress and vertical salt flux were largest at a midplume depth, where stratification and vertical shear were also high, consistent with shear-induced mixing. Internal stress slows the spreading plume considerably. A kinematic description of the spreading process relates lateral spreading to the momentum dynamics and illustrates that plume spreading is largely a competition between the cross-stream pressure gradient and Coriolis forces. However, the very near-field dome of buoyant water is instrumental in setting initial flow pathways.

Corresponding author address: Ryan M. McCabe, Department of Aviation, Old Main Building 205A, University of New South Wales, Sydney, NSW 2052, Australia. Email: r.mccabe@unsw.edu.au

Abstract

Momentum balances in the near-field region of a large, tidally pulsed river plume are examined. The authors concentrate on a single ebb tide of the Columbia River plume, using the Regional Ocean Modeling System (ROMS) configured to hindcast flow conditions on the Washington and Oregon shelves and in the Columbia River estuary. During ebb, plume-interior streamwise balances are largely between advection, pressure gradient, and frictional forces. Stream-normal balances in this region reduce to centrifugal, cross-stream pressure gradient, and Coriolis terms (i.e., the “gradient wind” balance commonly assumed in river plume bulge investigations). Temporal derivatives are most important at the plume front and as the ebb progresses. Winds were light and contributed little to the force balance. Midebb stress and vertical salt flux were largest at a midplume depth, where stratification and vertical shear were also high, consistent with shear-induced mixing. Internal stress slows the spreading plume considerably. A kinematic description of the spreading process relates lateral spreading to the momentum dynamics and illustrates that plume spreading is largely a competition between the cross-stream pressure gradient and Coriolis forces. However, the very near-field dome of buoyant water is instrumental in setting initial flow pathways.

Corresponding author address: Ryan M. McCabe, Department of Aviation, Old Main Building 205A, University of New South Wales, Sydney, NSW 2052, Australia. Email: r.mccabe@unsw.edu.au

1. Introduction

River plumes have received much interest in recent literature. Insight into how the buoyancy, momentum, chemical constituents (nutrients and pollutants), and sediment inputs provided by rivers affect the coastal ocean is vitally important for further understanding of regional productivity and ecosystem health. The most distinguishing property of a river plume is its buoyancy. Because of this buoyancy, any oceanic nutrients mixed into the plume may become trapped near the surface (for a “surface advected” plume, see Yankovsky and Chapman 1997). River-borne and oceanic nutrients may then fuel biological production (e.g., Lohan and Bruland 2006). Additionally, plumes provide a method for horizontal redistribution of nutrients and pollutants, because they may spread laterally (Kashiwamura and Yoshida 1967; Wright and Coleman 1971; Luketina and Imberger 1987), can advect material long distances as coastal currents (e.g., Anderson et al. 2005), and are quite susceptible to steering by the wind (e.g., Masse and Murthy 1990; Fong et al. 1997; Sanders and Garvine 2001; Whitney and Garvine 2005; Hickey et al. 1998, 2005; Choi and Wilkin 2007). Fong and Geyer (2001) and Lentz (2004) discuss the Ekman dynamics and associated mixing of a far-field plume under wind forcing. Our study, completed as part of the River Influences on Shelf Ecosystems (RISE) project, focuses on tidal dynamics of a large near-field plume.

a. The near-field region

Different physical processes may occur in the near-field, including “shoaling” or “lift-off” if the plume loses contact with the bottom (e.g., Hearn et al. 1985; MacDonald and Geyer 2004, 2005) and lateral spreading, because the plume is free of channel sidewalls (Kashiwamura and Yoshida 1967; Wright and Coleman 1971; Luketina and Imberger 1987). Near-field mixing is enhanced in the lift-off region (MacDonald and Geyer 2004) and at the offshore plume–ocean front (Luketina and Imberger 1989; Orton and Jay 2005; Nash and Moum 2005), where horizontal convergence drives downwelling (O’Donnell et al. 1998). Small-scale near-field flows are common in engineering literature, with many studies of power facility and sewage outfalls (e.g., Chen and MacDonald 2006). However, the near-field is also important for rotating geophysical flows, because this is the “turning” region a classical larger-scale plume must transit before flowing along the coastal wall as a far-field buoyant coastal current. On somewhat longer time scales (∼2–5 days), this turning region can harbor low-salinity water in a recirculating plume “bulge” (e.g., Chao and Boicourt 1986; Yankovsky and Chapman 1997) that may limit downstream coastal current transport (Fong and Geyer 2002; Horner-Devine et al. 2006). Recent field observations have documented bulge circulation off the Hudson (Chant et al. 2008) and Columbia Rivers (Horner-Devine 2009) during weak winds.

b. Columbia River plume background

The Columbia is a midlatitude, high-flow-rate, tidally dominated river in the U.S. Pacific Northwest. It is also the largest source of freshwater between San Francisco and the Juan de Fuca Strait. Discharge from the Columbia River varies between 3000 (late summer) and 17 000 m3 s−1 (spring) in a typical year, though these values are significantly less than historical flows (e.g., Naik and Jay 2005). The Columbia River mouth experiences large tides (1–3 m) of mixed semidiurnal character. During ebb, river-mouth near-surface velocities can approach 3 m s−1. The outflow is nominally oriented due west onto the shelf, resulting in part from the presence of two jetties. Typical scales for the estuary mouth are 3.5 km across and 15–20 m deep.

Wind forcing and ocean currents influence the plume on both interseasonal (Barnes et al. 1972; García Berdeal et al. 2002) and synoptic time scales (Hickey et al. 1998, 2005); and coastally-trapped waves are significant in this region (Battisti and Hickey 1984). Upwelling-favorable winds give rise to a southwestward-directed Columbia plume, whereas weak or downwelling-favorable winds force a classic coastal current (e.g., García Berdeal et al. 2002; Hickey et al. 2005, 2009) that flows north, opposite O(0.1 m s−1) ambient ocean currents in summer (Hickey 1989). Periods of intermittent winds can produce a “bidirectional” plume where northward- and southward-tending plume arms may coexist (Hickey et al. 2005, 2009). The bulk of historical Columbia River plume observations are contained in Barnes et al. (1972) and Hickey et al. (1998), with the latter being a 1990 winter study.

Based on recently observed salinity classes (Orton and Jay 2005; Horner-Devine et al. 2009; McCabe et al. 2008; Hickey et al. 2009) and the simulated mechanical energy budget of MacCready et al. (2009), one may expect as much as one-half to two-thirds of the mixing from fresh to oceanic water in the Columbia system to occur at sea. This highlights the importance of understanding the physical processes taking place in both the near- and far-field zones. Drifter observations (McCabe et al. 2008) helped delineate entrainment processes occurring in the tidal Columbia plume, but it remains difficult to fully describe near-field momentum balances from observations alone. We pursue this here by using realistic numerical simulations.

c. Paper outline

In this paper, we present analysis of momentum dynamics in the near-field region of the Columbia River plume and link lateral spreading rates kinematically to those dynamics. We focus on tidal time-scales of the ebb jet before it geostrophically adjusts into the plume bulge. Our results come from a realistic regional numerical model (section 2) designed to simulate the Columbia River estuary and its outflow onto the Washington and Oregon continental shelves. A simple test of model performance is presented in section 3, where we compare output, following numerical floats, to select June 2005 drifter observations obtained during the RISE field program. Simulated Columbia River plume momentum balances are then presented in section 4 from two perspectives: a plan view of the surface flow at different ebb-tide phases and from the point of view of surface-trapped parcels of plume water as they exit the estuary, similar to our drifter observations. Plume mixing is briefly discussed in section 5. Section 6 examines plume spreading and its relation to the momentum dynamics. We conclude with section 7.

2. Numerical model configuration

a. The model, bathymetry, and grid

We used the Regional Ocean Modeling System (ROMS; Rutgers University, version 2.2) for this study (Shchepetkin and Williams 2005). ROMS is a three-dimensional (3D), hydrostatic, finite-difference, free-surface model that incorporates a “stretched,” terrain-following vertical coordinate allowing for higher resolution near the surface and bottom boundaries (Haidvogel et al. 2000). Horizontal resolution is also adjustable, enabling increased grid density in regions of interest. ROMS solves the Reynolds-averaged, Boussinesq form of the Navier–Stokes equations. The model has been successful in a number of recent coastal (e.g., Marchesiello et al. 2003; Wilkin and Zhang 2007), river plume (Hetland 2005; Choi and Wilkin 2007; Zhang et al. 2009), and estuarine studies (Li et al. 2005; Warner et al. 2005a).

Numerical simulations with ROMS were completed to provide regional hindcasts for two RISE field seasons (summers of 2004 and 2005). Model configuration and predictability for our summer 2004 simulations are well documented in recent literature (e.g., MacCready et al. 2009; Liu et al. 2009a,b), with Liu et al. (2009b) providing a comprehensive discussion of model performance and skill. For the current study, a summer 2005 simulation was completed first, and hourly output from that run was used to restart smaller runs at times of interest. Aside from 2005 forcing (described later), our model incorporates improved Columbia River mouth U.S. Geological Survey (USGS) bathymetry not implemented in the 2004 simulations of MacCready et al. (2009) and Liu et al. (2009a,b). We introduced this change because model–data comparisons in the seaward portion of the estuary showed significant depth differences. The USGS dataset was merged with bathymetry from the National Geophysical Data Center (NGDC) Coastal Relief Model (Divins and Metzger 2002), and the result was smoothed for ROMS numerical stability (Haidvogel et al. 2000). Navigational channels in the Columbia River estuary were then redeepened in order to achieve a salt intrusion of the appropriate length. Because of our grid resolution, the Columbia River upstream of ∼50 km from sea is modeled as a straight channel 300 km long, 3 km wide, and 3 m deep. This design absorbs tidal energy, with almost none reaching the easternmost boundary.

The model domain (Fig. 1) was configured as a stretched spherical grid with ∼400-m resolution in the estuary and plume region. Horizontal resolution increases to ∼8 km away from the near-field zone. The resulting grid is 293 × 171 in the horizontal with 20 vertical layers. Vertical resolution in the surface water ranges from <1 m in the near-field and estuary to ∼5 m offshore.

b. River and tides

Daily average volumetric river flow and river temperature come from the Beaver Army Terminal gauging station (USGS 14246900) located ∼86 km upstream of the river mouth. Tidal forcing of surface height and depth-averaged velocity at the ocean boundaries are specified using 10 tidal constituents from the TPXO6.0 analysis (Egbert et al. 1994; Egbert and Erofeeva 2002). An example of model ebb-tide surface height and currents at the Columbia River mouth is shown in Fig. 2 for 9 June 2005, our period of interest. The model Columbia River outflow is highly variable near maximum ebb. The ∼20–30-min period variability in model currents was not present in previous runs lacking the USGS bathymetry. Because of this variability, we present ∼30 min temporal averages of flow properties in section 4.

c. Atmospheric forcing

Atmospheric forcing, including hourly 10-m wind, surface pressure, temperature, humidity, and radiation, was obtained from the 4-km regional forecast Northwest Modeling Consortium fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5; Mass et al. 2003). Tinis et al. (2006) provide an assessment of MM5 winds in the region. Surface fluxes of momentum and heat are calculated in ROMS using bulk formulations (Fairall et al. 1996a,b; Liu et al. 1979). Net shortwave radiation and downward longwave radiation are given as external forcing; then, upward longwave, sensible, and latent heat fluxes are calculated in the model. Evaporation and precipitation, as they affect salinity, were set to zero because we assumed their influences would be negligible when compared with Columbia River outflow.

d. Initial and boundary conditions

Model initial and open boundary conditions for tracers, velocity, and subtidal free-surface height come from the ∼9-km resolution Navy Coastal Ocean Model–California Current System (NCOM CCS) model (Shulman et al. 2004, 2007), which assimilates data and is nested within the ⅛° global NCOM model (Barron et al. 2006; Kara et al. 2006). Thus, some variability resulting from remote forcing, such as low-mode coastal-trapped waves, is included in our model. Open boundary conditions for the free surface and depth-averaged momentum are given by the Chapman (1985) and Flather (1976) formulations. Three-dimensional fields of velocity and tracers are treated with a radiation boundary condition (Marchesiello et al. 2001). Over a six-gridpoint-wide region on the open ocean boundaries, the T and S fields are relaxed to their NCOM CCS values: over 10 days at the boundary and increasing to 60 days at six points into the grid.

e. Turbulence closure

Finally, turbulence closure is given by the k − ε version of the generic length scale (GLS) formulation (Umlauf and Burchard 2003) with the Canuto A stability functions (Canuto et al. 2001). This parameterization includes shear-driven mixing. Sensitivity tests performed for the summer 2004 hindcast indicated that model skill was greatest at RISE mooring locations when using this scheme (Liu et al. 2009b). Because an estuary–plume–shelf model represents a severe test for any turbulence parameterization, it seems sensible to ask how well we might expect our model to perform. Next we briefly review some recent estuarine and plume applications aimed at testing such schemes.

Warner et al. (2005b) compare various turbulence parameterization schemes in ROMS for different physical scenarios. Their results showed very minor differences between the standard GLS options, although they did note enhanced sensitivity of suspended sediment concentrations between the closures in a model estuary. Other recent studies have examined the influence of turbulence parameterizations for realistic estuarine simulations using ROMS (e.g., Warner et al. 2005a; Li et al. 2005). Top-to-bottom salinity differences and temporal evolution of both currents and salinity were predicted accurately by the Hudson River estuary model of Warner et al. (2005a), but the vertical salinity structure was too smooth when compared to observations. Again, results varied little when altering the turbulence closure method. Li et al. (2005) also noted a weaker-than-observed stratification in their Chesapeake Bay model, particularly during periods of high runoff. Here too, little differences resulted among turbulence schemes. Results of Li et al. (2005) instead showed a strong dependence on the background diffusivity, with the best predictability obtained when using a small vertical diffusivity of O(10−5 m2 s−1) or less. However, even with a diffusivity of 10−6 m2 s−1, vertical stratification was still too weak, pointing to deficient turbulence parameterization for strongly stratified flows. A recent study by MacDonald et al. (2007) incorporates an extremely high-resolution (20 m horizontal; more than 14 levels above 2-m depth in the vertical) ROMS simulation of the near-field Merrimack River plume for comparison with control-volume-inferred and direct turbulent dissipation measurements. Insignificant differences between the various GLS closure schemes were found in their simulations, and only slight modifications were reported when altering the choice of stability functions. Model results compared well with their field measurements, correctly reproducing a two-decade decrease in dissipation away from the river mouth. However, because of observational limitations, dissipation comparisons shallower than the σt = 19 kg m−3 level were not fully presented. This very near-surface zone represents a key challenge in field measurements. In this regard, more studies similar to MacDonald et al. (2007) are needed.

We proceed with our own Columbia River plume simulations, keeping these possible numerical shortcomings in mind. We set the background vertical diffusivity of both tracers and momentum at 5 × 10−6 m2 s−1, with zero explicit horizontal diffusivity and viscosity (e.g., Dong et al. 2007). Bottom stress is parameterized with a quadratic drag law and a drag coefficient of 3 × 10−3 (e.g., Geyer et al. 2000).

3. Model testing: Comparing model floats to observed drifter data

This paper relies on numerical simulations to analyze river plume dynamics. Even though the model was designed to hindcast flow for the estuary–shelf system, we do not expect a perfect reproduction. This section attempts to provide evidence that the model faithfully reproduces bulk flow features of the Columbia River plume by comparing numerical output with a single RISE drifter experiment.

A drifter experiment from 9 June 2005, where four surface-configured (top 1 m) drifting buoys (e.g., Davis 1985) were deployed across the Columbia estuary mouth near maximum ebb (∼2.8 m s−1 surface currents), serves as our basis of comparison (McCabe et al. 2008). Drifter tracks from that 2005 field deployment are shown in Fig. 3a as thick gray lines and are overlaid with ROMS surface float tracks (colored by salinity); both the field and model tracks are 8 h in duration. Clearly, all drifters spread apart, their recorded salinities (Fig. 3b) increase, and they decrease in speed (Fig. 3c) as they move offshore. Drifter-measured salinities increase rapidly near the estuary mouth, where entrainment is large O(10−3 m s−1), but then change more gradually as the drifters move offshore (McCabe et al. 2008). Model floats for this comparison were released ∼2 km upstream of the field deployment sites but pass those sites ∼10 min after field release times. Model floats released 15 min earlier showed only slight differences in flow patterns compared to Fig. 3a, implying that model–data comparisons are valid for the chosen releases.

Significant differences exist between the model and field drifter deployments. Model floats do not penetrate as far seaward as the field drifters (Fig. 3a), and they track more saline water (Fig. 3b), with a mean salinity excess of ∼3–4. Average model and field drifter speeds (Fig. 3c) show similar trends, though the float track comparisons themselves best illustrate the lasting effects of flow discrepancies.

In spite of the differences outlined, model–data comparisons are also encouraging. Model floats released at the estuary mouth show the same basic flow structure, including lateral spreading. Similarly, float-tracked water becomes progressively more saline as it moves seaward, and float speeds decrease with time in a fashion similar to the data. Thus, although some details of the model output are lacking, the model does reproduce important characteristics of the near-field Columbia River plume. In the next section, we use the model to analyze plume outflow dynamics, which we assume are representative of actual balances in the field.

4. Model momentum balances

a. Previous work

Here, we use model output to explore the dynamics of a single freshwater Columbia River ebb pulse from 9 June 2005. We follow Hench and Luettich (2003) and analyze momentum terms in a streamwise–normal (sn) coordinate system. Their study examined depth-averaged tidal flow issuing from idealized and realistic coastal inlets. They found that momentum balances were highly localized in inlets and extremely variable with tidal phase. Along-stream balances were largely between advection, pressure gradient forces, and bottom friction, whereas centrifugal and pressure gradient forces dominated in the cross-stream direction. The Coriolis force was unimportant and temporal derivatives were only influential near slack conditions, a time when cross-inlet exchange became possible because of local dynamical balances. Shipboard acoustic Doppler current profiler (ADCP) observations by Vennell (2006) subsequently confirmed the numerical work of Hench and Luettich (2003), though bottom friction was relatively small at that field site.

Our stratified plume shares similarities with these inlet studies, and we have arranged our figures to facilitate comparisons between our study and that of Hench and Luettich (2003). However, because the Columbia plume is stratified and loses contact with the bottom, we expect different dynamics. We will briefly introduce the streamwise–normal coordinate system used to interpret our results and then discuss momentum balances in that coordinate system. ROMS calculates exact momentum diagnostics by averaging terms in the momentum equations over a user-specified duration. Balances presented were averaged over four time steps in the model, and we then averaged results over nine output files (∼31 min) as an attempt at masking the influences of model Columbia River outflow variability (Fig. 2).

b. Streamwise–normal coordinate system

A local streamwise–normal coordinate system may be defined such that the coordinate directions are aligned with instantaneous velocity vectors at each model grid cell. The s direction is naturally defined as positive in the direction of flow. With z positive upward in a right-handed system, the stream-normal direction n is defined as positive left of the flow. The resulting streamwise velocity Us at any place and time is then just the flow speed, whereas the stream-normal component of the flow Un = 0 everywhere. This coordinate system can help simplify dynamical understanding in curved flows. However, frictional terms become more complicated and care must be taken in low-flow situations where speeds are small and flow direction changes rapidly. Results can also be tricky to understand without knowledge of the flow field. For this reason, our figures include spatial vector fields of the surface flow for reference. Transformation into the sn system requires a coordinate rotation for all grid points and times of interest. We forego a detailed derivation of the Cartesian (xy) to streamwise–normal (sn) momentum transformation and instead refer the reader to the presentation in the appendix of Hench and Luettich (2003).

The horizontal momentum equations in streamwise and stream-normal components, respectively, are
i1520-0485-39-11-2839-e1
i1520-0485-39-11-2839-e2
where we have included physical interpretations beneath each momentum term. We have omitted horizontal viscous terms, because our simulations lacked explicit horizontal viscosity and instead relied on “numerical diffusion” (e.g., Dong et al. 2007). Here, time is written as t; the hydrostatic pressure is written as P; water density is written as ρ, with ρ0 as a constant reference density; f is the Coriolis parameter; and τ(s) and τ(n) are the s and n components of stress, respectively. The streamline angle α = α(x, y, t) is calculated from horizontal Cartesian velocity components (u, υ) as α = arctan(υ/u). Vertical velocity is w. Streamline curvature 1/Rs = ∂α/∂s defines the local radius of curvature Rs. Equations (1) and (2) are equivalent to those provided by Hench and Luettich (2003), except we have retained vertical advection and a generalized vertical stress divergence instead of considering only bottom stress. With this approach, stress terms may include surface wind stress and internal shear stress in addition to the bottom stress. We next present momentum balances for a Columbia River ebb-tide pulse in sn coordinates.

c. Near maximum ebb

Plan views of salinity (Fig. 4b), surface height anomaly (Fig. 4d), surface flow vectors (Fig. 4e), and different terms in the s (Figs. 4f–j) and n (Figs. 4k–o) momentum equations just after maximum ebb but before tidal currents at the mouth (Fig. 4a) have started to relax are shown in Fig. 4. A vertical section of salinity (Fig. 4c) taken along the dashed white line in Fig. 4b is also included. Momentum terms in Figs. 4f–o correspond to the surface layer of the model grid. At this tidal phase (Fig. 4a), the bulk of low-salinity water has only just started flowing onto the shelf (Figs. 4b,e), detaching from the bottom near 124.15°W (Fig. 4c). It takes some time for freshwater to exit the river mouth on ebb because ambient water is drawn into the estuary on flood. The new ebb pulse is identifiable as a tongue of elevated surface height (Fig. 4d) extending beyond the estuary mouth. The plume also has a distinct front, perhaps best illustrated by the local acceleration term (Fig. 4f) but is also evident as an offshore ribbon of excess surface height (Fig. 4d). Even after temporal averaging (∼30 min), momentum terms appear somewhat noisy, but bulk patterns are still discernable. Time derivatives in the s and n directions appear largest and are best organized at the front where velocities change rapidly in both magnitude and direction (Figs. 4f,k). Low-salinity water far up the estuary advectively accelerates seaward (Figs. 4e,g) under the negative streamwise pressure gradient (Fig. 4h); for the model’s top layer, this largely results from the surface height field. A channel constriction is encountered near 124°W, and the flow briefly decelerates as the channel widens west of this point (Fig. 4g). The flow again accelerates in a north–south band near the jetty tips and near the lift-off point (Fig. 4c), but it largely decelerates once at sea (Fig. 4g), as the tongue of excess surface height relaxes (Fig. 4d). The narrow band of streamwise acceleration at the jetty tips (and smaller one near lift-off) coincides with the downstream side of the estuary mouth surface height dome (Fig. 4d) and negative streamwise pressure gradient (Fig. 4h). Friction is highly elevated near the estuary mouth and remains significant in the plume interior (Fig. 4j), even after the plume has detached from the bottom (discussed further in the next section). By definition, the streamwise Coriolis force (Fig. 4i) is zero.

The estuarine cross-stream momentum balance is most interesting west of 124°W, where the surface flow is turning anticlockwise (i.e., primarily centrifugal, not shown) to exit the channel (Fig. 4l) and water is piled up on the channel’s north side, giving rise to a southward cross-stream pressure gradient (Fig. 4m). A dramatic adjustment in the surface height slope (Figs. 4d,m) occurs as the plume leaves the channel. At the jetties, the cross-stream pressure gradient switches from largely negative to nearly symmetric about the northern channel (Fig. 4m), because there is no longer a channel sidewall for the flow to lean against. The dome of low-salinity water thus slumps to the north and south (Figs. 4d,m), with the middle peak in surface height serving as a barotropic “dynamical wall” (Hench and Luettich 2003). Plume water north or south of the dome’s central axis would be expected to stay north or south. A clear correspondence exists between the (primarily) centrifugal (Fig. 4l) and cross-stream pressure gradient terms (Fig. 4m). The outflowing plume turns anticyclonically (clockwise) on the north side and cyclonically (anticlockwise) on the south side (Fig. 4l). However, the Coriolis force (Fig. 4n) is also large and cannot be neglected. This differs from the study of Hench and Luettich (2003), where the Coriolis force played an insignificant dynamical role. Stream-normal friction (Fig. 4o) matters very little to the dynamics.

We summarize maximum ebb conditions as follows: the estuarine streamwise momentum balance is between the pressure gradient driving the low-salinity water seaward, streamwise advection of the flow, and the retarding force of friction, with the latter very important near the estuary mouth. After the plume is free of the channel the same basic balance exists, with both the streamwise pressure gradient and friction largest near the estuary mouth and lift-off. Local acceleration is largest near the ocean–plume front, but our model also indicates that this term may be significant near the estuary mouth. Field measurements (e.g., MacDonald and Geyer 2004), however, indicate that this term should be relatively unimportant near maximum ebb. Stream-normal momentum balances are dominated by advective acceleration, cross-stream pressure gradients, and the Coriolis force. Temporal changes in flow direction are generally minor everywhere, except at the ocean–plume front.

d. Midebb

Midebb flow properties appear in Fig. 5. Tidal currents at the estuary mouth (Fig. 5a) have relaxed considerably from maximum ebb. Seven surface float tracks (gray lines), released across the mouth at maximum ebb (Fig. 4), are included in Fig. 5. Black dots represent current float positions. Float behavior is similar to Fig. 3 but release times were ∼0.5 h later. This delay ensured lower plume salinities (closer to field data) and allowed the plume to penetrate farther seaward.

At this phase, tidal plume fronts have expanded seaward and a large bolus of low-salinity water exists over the shelf (Fig. 5b). No term (other than Coriolis) in the streamwise momentum budget can be neglected with certainty (Figs. 5f–j). The plume interior is still largely decelerating (Fig. 5g), though positive streamwise acceleration and a negative streamwise pressure gradient band is still evident at the mouth (Figs. 5g,h), coincident with plume lift-off (Fig. 5c). Beyond this zone, the plume interior shows a slightly positive (adverse) streamwise pressure gradient (Fig. 5h). The outflow is also decelerating in time (Fig. 5f), although flow directions show little organized change (Fig. 5k) away from the front. Of particular interest is the friction term (Fig. 5j), which remains significant away from the estuary mouth. Overall, streamwise dynamics are similar to the barotropic inlet studies of Hench and Luettich (2003). The major difference is that bottom friction remained important in their study, whereas the surface-advected plume experiences a primarily streamwise internal stress beyond lift-off (discussed in section 5).

The stream-normal momentum balance remains similar to that near maximum ebb (advection, pressure gradient, and Coriolis). However, it is now apparent that the advection (Fig. 5l) and cross-stream pressure gradient terms (Fig. 5m) are no longer symmetric with respect to the estuary’s northern channel. An anticyclonic turning of the flow and largely positive cross-stream pressure gradient are dominant in the plume interior. Planetary rotation remains of primary importance (Fig. 5n), whereas stream-normal stress (Fig. 5o) matters little.

e. Slack conditions

Slack conditions (Fig. 6) are encountered ∼2 h after the previous snapshot and at least 4 h after maximum ebb (Fig. 6a). Just beyond slack, surface water is increasingly accelerating up estuary (Figs. 6e,f) in response to the now favorable up-estuary pressure gradient that extends slightly seaward of the mouth (Fig. 6h). Surface flow just outside the mouth turns into the estuary (Fig. 6e). As with the tidal inlet study of Hench and Luettich (2003), the momentum jet gets “pinched off” at the estuary mouth by nearshore flooding water. In our case, much of this water comes from the north and is still relatively buoyant. This process is captured best in the streamwise momentum balance (Figs. 6f–j). Surface floats released near maximum ebb have traversed the plume and are near the ocean–plume boundary, turning back toward land. The offshore plume interior is still slowing down (Fig. 6f) under the influence of an adverse streamwise pressure gradient (Fig. 6h) and significant streamwise friction (Fig. 6j).

A nonzero cross-stream pressure gradient is barely visible in the offshore plume (Fig. 6m), forcing the plume’s lateral spreading. Near the jetty tips, a cross-stream centrifugal-pressure gradient balance is just beginning to set up as flooding water enters the estuary (Figs. 6l,m). This balance continues to build at the mouth, becoming more dominant as the tidal cycle advances (not shown).

f. Surface float momentum balances

We have presented snapshots (∼30-min averages) of surface flow properties and momentum balances for a single ebb pulse of plume water. Here, we further the discussion by including momentum balances from the point of view of surface floats released across the estuary mouth near maximum ebb.

The surface salinity field from Fig. 6 (near slack conditions) is reproduced in Fig. 7a with model surface float tracks overlaid. Three of the float tracks (north, central, and south) are highlighted magenta, and sn momentum balances following those floats are included in Figs. 7b–d. Consider the central float (Fig. 7c): for brevity, we describe the momentum balances for this float, calling attention to differences exhibited by other floats. The central float’s streamwise momentum balance is largely an advection–friction balance (blue and red lines) with early modifications resulting from the streamwise pressure gradient (green) and temporal derivative (dotted black). As this float moves offshore from its release point, the plume is still in contact with the bottom (Fig. 4c), and the surface water experiences a relatively large frictional stress (Figs. 4j, 7c). This stress decreases past the 5-km along-track mark but remains nonzero as the plume lifts away from the bottom. The early streamwise pressure gradient (green) and advective terms (red) mimic each other. This is the Bernoulli-like acceleration experienced by the float as it traverses the surface height dips described earlier (Figs. 4g,h). Beyond these major surface deformations, the streamwise balance reduces to an advection–friction balance, with an additional slowing influence from the positive pressure gradient field. The time derivative term changes sign in the offshore plume, reflecting its spatially patchy nature (Fig. 5f), but we generally expect this term to become more important as the floats near the plume front.

The early stream-normal momentum balance (central float; Fig. 7c) shows a “cyclostrophic” (e.g., Holton 1992) response (red and green lines) to the rapidly adjusting pressure field (Figs. 4l,m). However, as described earlier, the Coriolis acceleration (solid black line) cannot be neglected. There is a short-lived change in the rotary acceleration term (dotted black line) near the estuary mouth; otherwise, that term remains small. The cross-stream pressure gradient force (green) also becomes relatively unimportant after lift-off (i.e., after ∼6 km). This is simply because the chosen float is near the center of the outflowing plume where the cross-plume surface height is flat. Beyond lift-off, the primary normal-direction balance is between the centrifugal (red) and Coriolis acceleration (black) terms for the central float.

Other model floats released north (Fig. 7b) and south (Fig. 7d) of the central float show varying degrees of similarity to the balances just described. Streamwise balances generally agree well, except that local temporal accelerations can dominate for floats too near the plume edge (not shown). North–south differences in the stream-normal momentum balance are perhaps more interesting. Here (Figs. 7b,d), the influence of the cross-stream pressure gradient (green) is apparent: positive north and negative south. For the northern float (Fig. 7b), the positive stream-normal pressure gradient (green) adds to the Coriolis term (black), requiring a much larger (negative) advective acceleration (red). To the south (Fig. 7d), the Coriolis (black) and stream-normal pressure gradient (green) are of opposite signs, and the centrifugal term (red) is much smaller in the plume. This balance is discussed further in section 6.

5. Near-field plume mixing

The near-field dynamics described in section 4 showed significant frictional stress in the plume interior that persisted throughout the ebb cycle (Figs. 4j, 5j, 6j, 7). To investigate this we briefly examine midebb sections (∼31-min averages) of salinity S, vertical shear ∂Us/∂z, vertical stress KVUs/∂z, and vertical salt flux −KSS/∂z (Fig. 8). Momentum balances at this time are shown in Fig. 5.

At midebb, the model plume extends seaward over 15 km and the lift-off region has moved ∼5 km upstream to very near the float release locations (Figs. 5b,c). A large mass of low-salinity water exists over the shelf (Fig. 5b), and the plume interior is decelerating under the combined effects of an adverse streamwise pressure gradient force (Fig. 5h) and frictional stress (Fig. 5j). The plume is vertically sheared with the largest shears at mid-depth (Fig. 8b), where stratification is high. Vertical stress (Fig. 8c) is also largest midway through the plume, though somewhat patchy. Farther up estuary, stress values are exceedingly large, consistent with bottom boundary influences. A plot of applied surface wind stress is not shown, but a typical value for this experiment is <0.03 Pa (for a 4 m s−1 wind speed), an order of magnitude smaller than the stress values in the plume (Fig. 8c). If stress in the plume resulted only from the applied wind forcing, a vertical profile would show stress values decreasing from the surface with increasing depth (e.g., Fong and Geyer 2001). This is not the case in our simulations. Rather, stress in the near-field plume reaches values over 2 times larger than a 7.5 m s−1 wind (∼0.1 Pa) would impose. Frictional stress in the midebb near-field plume is primarily an internal stress arising from instabilities of the sheared stratified flow. This vertical flux of low momentum fluid into the plume slows the plume considerably (Figs. 5, 7). Additionally, our simulations show extremely large bottom stresses throughout the estuary that may attach with lift-off earlier in the ebb. Such processes and their implications are discussed in detail with recent Columbia River estuary observations by Nash et al. (2009).

The vertical turbulent flux of salt into the plume O(10−3 m s−1) is also largest where stratification and vertical shear are high (Fig. 8), consistent with shear-induced mixing. This is not surprising, considering the extremely large O(2–3 m s−1) tidal velocities at the Columbia River mouth. Although plume mixing is highest near the estuary mouth, a large portion also takes place throughout the interior Columbia plume. For comparison, Fong and Geyer (2001) found O(10−5 m s−1) vertical turbulent salt flux values in their numerical study of a wind-forced coastal current 2 orders of magnitude smaller than our near-field Columbia plume estimates. However, because of the large difference in spatial extent between near- and far-field plumes, wind-induced mixing may ultimately contribute a comparable or even greater buoyancy flux (MacCready et al. 2009).

6. Plume spreading

The midebb near-field mixing discussed above is primarily a streamwise property of the sheared stratified flow (e.g., Richardson number dependent) that decelerates the plume and decreases its buoyancy anomaly. Vertical mixing occurs over an increasingly large area (Fig. 5j), because the plume spreads laterally. Few studies have addressed buoyant plume spreading; notable exceptions are Wright and Coleman (1971) and recent work by Hetland and MacDonald (2008). Wright and Coleman (1971) suggested that a laterally homogeneous plume should spread at twice the internal gravity wave speed. They included the factor of 2, because the plume was to spread equally in two directions.

We approach plume spreading by appealing to the dynamics in section 4. First, consider two adjacent water parcels (e.g., tagged with surface drifters) at a given time t having instantaneous velocity vectors and . Each vector is written in Cartesian vector and complex notations. Cartesian components (u, υ) are in the (x, y) directions with unit vectors . Complex notation relates the velocity magnitudes U1 and U2 with the local instantaneous streamline angles α1 and α2. At time t, water parcels are separated by a distance vector B(t), and we allow them to spread apart from each other over an interval of time (Fig. 9). A “rate of spreading” vector may be defined as the difference of the two velocity vectors:
i1520-0485-39-11-2839-e3
where D/Dt indicates that we are following the parcels. The resultant vector magnitude can be written in terms of the individual velocity vector magnitudes and streamline angles using the law of cosines:
i1520-0485-39-11-2839-e4
The vector’s angle is
i1520-0485-39-11-2839-e5
Both quantities are easily obtained from surface Lagrangian drifter measurements. However, the vector magnitude in Eq. (4) is of primary interest for quantifying the spreading rate. Consider a short example: if two adjacent velocity vectors point in the same direction (i.e., they have the same streamline angles), then the cosine in Eq. (4) is unity and the rate of spreading depends only on the difference in water parcel speeds dU = U2U1. For this case, if there is no difference in speed, then there is no spreading. A nonzero angular difference obviously results in more spreading. In this way, the rate of spreading is influenced by both streamwise and stream-normal processes. One method for evaluating the relative importance of the streamwise and stream-normal components is to integrate (in a Lagrangian sense) Eqs. (1) and (2) along the float trajectories to obtain equations for Us and α in terms of the dynamics
i1520-0485-39-11-2839-e6
i1520-0485-39-11-2839-e7
We can further time integrate the rate of spreading itself to arrive at the separation distance between two adjacent drifters
i1520-0485-39-11-2839-e8
another quantity easily calculated from model or field drifter data. Equation (8) links the separation distance to the dynamics when Eqs. (6) and (7) are used in Eq. (4). The separation distance between adjacent floats B is presented in Fig. 10 (thick black line) as a function of time for the different float pairs of Fig. 7. Each panel also includes the amount of float separation resulting from streamwise velocity differences between the two floats (gray line) and from differences in flow direction (thin black line), the stream-normal property. Angular dependence was calculated as the residual of the total spreading less the amount resulting from speed differences. This is because in the example cited earlier (where no angular dependence was considered) speed influences could be decoupled from angular effects in Eq. (4). Assuming only angular dependence does not decouple the two. Very little spreading occurs between the second float pair, counting from the south side (Figs. 7a, 10b); most of that spreading results from streamwise flow differences. In this region, there is a negative stream-normal surface pressure gradient that is just large enough to offset the Coriolis force (Fig. 7d). Angular changes are small, because neither force effectively turns the floats. This is why there is little spreading along the float pathways until the floats near the plume edge. Now consider the north side of the plume, where most of the spreading occurs before reaching the plume front (Fig. 7a). Angular differences dominate spreading here (Figs. 10e,f). Examining the stream-normal balances in Figs. 7b,c explains why this is so. The central float (Fig. 7c) encounters a near-zero cross-stream pressure gradient; the plume is locally flat. This float is turned north by the Coriolis force (Fig. 7a) with little resistance. Floats to the north experience a Coriolis force of similar magnitude, but here an additional positive cross-stream pressure gradient exists (Fig. 7b). Because these two forces are additive, floats are turned an even greater amount, resulting in a large amount of spreading in the north plume (Figs. 10e,f). Frictional stress contributes little to the stream-normal surface momentum balance (Figs. 4o, 5o, 6o, 7), and it is clear that the important quantity for plume spreading is . When this quantity is zero, little spreading occurs. To get significant “leftward” spreading a negative stream-normal pressure gradient must overcome the rightward tendency of the Coriolis force. Rightward flow spreading is “easier,” because the two forces share the same sign on that side of the plume. Even with a symmetric normal-direction pressure gradient distribution, plume spreading is expected to be asymmetric because of the Coriolis force. This is echoed in the stream-normal momentum balances (e.g., Fig. 5). Note too that streamwise stress will impact plume spreading, because it changes both the flow speed and pressure gradients through vertical mixing.

Immediately after release, all float pairs except for the fifth pair indicate that streamwise velocity differences result in more spreading than flow direction does. This is not easily seen in Fig. 10, because floats were released at the estuary mouth, but it is consistent with the largely unidirectional river outflow at that location. However, floats quickly move seaward and encounter the surface height dome just offshore of the estuary mouth (Fig. 4d). This dome influences the streamwise and stream-normal dynamics considerably. To illustrate this, cumulative along-track integrals of the stream-normal surface pressure gradient (thick gray line) and Coriolis (thick black line) forces for three floats spanning the plume are shown in Fig. 11 (along with the frictional contribution). All floats indicate a significant influence from the normal-direction pressure gradient when crossing the surface height dome early after release. The pressure term quickly ramps up for the northern and southern floats (Figs. 11a,c), steering them right and left, respectively. Normal-direction pressure gradient and Coriolis forcing are of equal importance early on for the central float (Fig. 11b), but the pressure term contributes little after the initial hour (i.e., after that float has traversed the surface height dome; Figs. 4, 5, 7). Thus, the near-field surface height dome is instrumental in setting the initial float pathways.

7. Summary and conclusions

This paper discusses results obtained from realistic numerical simulations of the Columbia River plume. Our model was designed to hindcast circulation over the Washington and Oregon shelves and in the Columbia River estuary and plume, and we used it to examine dynamical properties of a single ebb-tide pulse of low-salinity water. Comparisons to surface drifter field observations illustrated some limitations of the model. Most notably, the model plume appeared too saline and did not penetrate as far seaward as observations indicated it should. Otherwise, model surface floats did show general agreement with field data: float salinities increased as they transited the plume, their speeds decreased, and they spread laterally, similar to the observations.

This study is important in three ways. First, it provided a description of the near-field plume momentum balances throughout the ebb tide. Plume-interior streamwise balances were largely between advective, pressure gradient, and stress terms. Normal-direction momentum balances reduced to centrifugal, pressure gradient, and Coriolis forces (the “gradient wind” or “cyclostrophic” balance that is commonly used in river-plume bulge investigations; Yankovsky and Chapman 1997; Horner-Devine et al. 2006). Temporal derivatives were most important at the ocean plume front and as the ebb progressed toward slack tide. Beyond midebb, ignoring any term in the streamwise momentum balance may be questionable.

Our results also highlighted the importance of interior plume stress. Internal friction is one of the primary forces acting to slow the near-field plume. We were able to easily illustrate this, because surface wind stress was negligible. Wind forcing could be important in the near-field for stresses larger than were considered here (e.g., ∼0.2 Pa). Stress and vertical salt flux in our simulations were largest at a midplume depth, where stratification and vertical shears were also high, consistent with shear-induced mixing.

Finally, we provided a kinematic description of tidal plume spreading that relates it to momentum dynamics in the near field. Plume spreading results from both streamwise and stream-normal properties of the flow, but it was typically largest where angular differences across fluid parcels were of primary importance. This seemingly simple result illustrates that plume spreading is largely a competition between the cross-stream pressure gradient and Coriolis forces. Because of the large stream-normal pressure gradients near the river mouth associated with the outflow of buoyant water (i.e., the large dome in excess surface height), the very near-field region dictates initial outflow directions and thereby impacts lateral spreading considerably.

Acknowledgments

We would like to express our gratitude to David Darr, who helped considerably with the numerical modeling component of this work, and to Yonggang Liu, who modified and ran the seasonal simulations. Amoreena MacFadyen and Philippe Estrade provided helpful discussion, and comments from two anonymous reviewers substantially improved the manuscript. This work was supported by the National Science Foundation as part of the CoOP RISE Program under OCE 0239089.

REFERENCES

  • Anderson, D. M., , B. A. Keafer, , W. R. Geyer, , R. P. Signell, , and T. C. Loder, 2005: Toxic Alexandrium blooms in the western Gulf of Maine: the plume advection hypothesis revisited. Limnol. Oceanogr., 50 , 328345.

    • Search Google Scholar
    • Export Citation
  • Barnes, C. A., , A. C. Duxbury, , and B. A. Morse, 1972: Circulation and selected properties of the Columbia River effluent at sea. The Columbia River Estuary and Adjacent Ocean Waters, A. T. Pruter and D. L. Alverson, Eds., University of Washington Press, 41–80.

    • Search Google Scholar
    • Export Citation
  • Barron, C. N., , A. B. Kara, , P. J. Martin, , R. C. Rhodes, , and L. F. Smedstad, 2006: Formulation, implementation and examination of vertical coordinate choices in the Global Navy Coastal Ocean Model (NCOM). Ocean Modell., 11 , 347375. doi:10.1016/j.ocemod.2005.01.004.

    • Search Google Scholar
    • Export Citation
  • Battisti, D. S., , and B. M. Hickey, 1984: Application of remote wind-forced coastal trapped wave theory to the Oregon and Washington coasts. J. Phys. Oceanogr., 14 , 887903.

    • Search Google Scholar
    • Export Citation
  • Canuto, V. M., , A. Howard, , Y. Cheng, , and M. S. Dubovikov, 2001: Ocean turbulence. Part I: One-point closure model—Momentum and heat vertical diffusivities. J. Phys. Oceanogr., 31 , 14131426.

    • Search Google Scholar
    • Export Citation
  • Chant, R. J., , S. M. Glenn, , E. Hunter, , J. Kohut, , R. F. Chen, , R. W. Houghton, , J. Bosch, , and O. Schofield, 2008: Bulge formation of a buoyant river outflow. J. Geophys. Res., 113 , C01017. doi:10.1029/2007JC004100.

    • Search Google Scholar
    • Export Citation
  • Chao, S-Y., , and W. C. Boicourt, 1986: Onset of estuarine plumes. J. Phys. Oceanogr., 16 , 21372149.

  • Chapman, D. C., 1985: Numerical treatment of cross-shelf open boundaries in a barotropic coastal ocean model. J. Phys. Oceanogr., 15 , 10601075.

    • Search Google Scholar
    • Export Citation
  • Chen, F., , and D. G. MacDonald, 2006: Role of mixing in the structure and evolution of a buoyant discharge plume. J. Geophys. Res., 111 , C11002. doi:10.1029/2006JC003563.

    • Search Google Scholar
    • Export Citation
  • Choi, B., , and J. L. Wilkin, 2007: The effect of wind on the dispersal of the Hudson River Plume. J. Phys. Oceanogr., 37 , 18781897.

  • Davis, R. E., 1985: Drifter observations of coastal surface currents during CODE: The method and descriptive view. J. Geophys. Res., 90 , (C3). 47414755.

    • Search Google Scholar
    • Export Citation
  • Divins, D. L., , and D. Metzger, cited. 2002: NGDC/MGG-Coastal Relief Model. [Available online at http://www.ngdc.noaa.gov/mgg/coastal/crm.html].

    • Search Google Scholar
    • Export Citation
  • Dong, C., , J. C. McWilliams, , and A. F. Shchepetkin, 2007: Island wakes in deep water. J. Phys. Oceanogr., 37 , 962981.

  • Egbert, G. D., , and S. Y. Erofeeva, 2002: Efficient inverse modeling of barotropic ocean tides. J. Atmos. Oceanic Technol., 19 , 183204.

    • Search Google Scholar
    • Export Citation
  • Egbert, G. D., , A. Bennett, , and M. Foreman, 1994: TOPEX/Poseidon tides estimated using a global inverse model. J. Geophys. Res., 99 , (C12). 2482124852.

    • Search Google Scholar
    • Export Citation
  • Fairall, C. W., , E. F. Bradley, , J. S. Godfrey, , G. A. Wick, , J. B. Edson, , and G. S. Young, 1996a: Cool-skin and warm-layer effects on sea surface temperature. J. Geophys. Res., 101 , (C1). 12951308.

    • Search Google Scholar
    • Export Citation
  • Fairall, C. W., , E. F. Bradley, , D. P. Rogers, , J. B. Edson, , and G. S. Young, 1996b: Bulk parameterization of air-sea fluxes for Tropical Ocean-Global Atmosphere Coupled-Ocean Atmosphere Response Experiment. J. Geophys. Res., 101 , (C2). 37473764.

    • Search Google Scholar
    • Export Citation
  • Flather, R. A., 1976: A tidal model of the northwest European continental shelf. Mem. Soc. Roy. Sci. Liege, 6 , 141164.

  • Fong, D. A., , and W. R. Geyer, 2001: Response of a river plume during an upwelling favorable wind event. J. Geophys. Res., 106 , (C1). 10671084.

    • Search Google Scholar
    • Export Citation
  • Fong, D. A., , and W. R. Geyer, 2002: The alongshore transport of freshwater in a surface-trapped river plume. J. Phys. Oceanogr., 32 , 957972.

    • Search Google Scholar
    • Export Citation
  • Fong, D. A., , W. R. Geyer, , and R. P. Signell, 1997: The wind-forced response on a buoyant coastal current: Observations of the western Gulf of Maine plume. J. Mar. Syst., 12 , 6981.

    • Search Google Scholar
    • Export Citation
  • García Berdeal, I., , B. M. Hickey, , and M. Kawase, 2002: Influence of wind stress and ambient flow on a high discharge river plume. J. Geophys. Res., 107 , 3130. doi:10.1029/2001JC000932.

    • Search Google Scholar
    • Export Citation
  • Geyer, W. R., , J. H. Trowbridge, , and M. M. Bowen, 2000: The dynamics of a partially mixed estuary. J. Phys. Oceanogr., 30 , 20352048.

  • Haidvogel, D. B., , H. G. Arango, , K. Hedstrom, , A. Beckmann, , P. Malanotte-Rizzoli, , and A. F. Shchepetkin, 2000: Model evaluation experiments in the North Atlantic Basin: Simulations in nonlinear terrain-following coordinates. Dyn. Atmos. Oceans, 32 , 239281.

    • Search Google Scholar
    • Export Citation
  • Hearn, C. J., , J. R. Hunter, , J. Imberger, , and D. van Senden, 1985: Tidally induced jet in Koombana Bay, Western Australia. Aust. J. Mar. Freshwater Res., 36 , 453479.

    • Search Google Scholar
    • Export Citation
  • Hench, J. L., , and R. A. Luettich Jr., 2003: Transient tidal circulation and momentum balances at a shallow inlet. J. Phys. Oceanogr., 33 , 913932.

    • Search Google Scholar
    • Export Citation
  • Hetland, R. D., 2005: Relating river plume structure to vertical mixing. J. Phys. Oceanogr., 35 , 16671688.

  • Hetland, R. D., , and D. G. MacDonald, 2008: Spreading in the near-field Merrimack River plume. Ocean Modell., 21 , 1221. doi:10.1016/j.ocemod.2007.11.001.

    • Search Google Scholar
    • Export Citation
  • Hickey, B. M., 1989: Patterns and processes of circulation over the Washington continental shelf and slope. Coastal Oceanography of Washington and Oregon, M. R. Landry and B. M. Hickey, Eds., Elsevier, 41–115.

    • Search Google Scholar
    • Export Citation
  • Hickey, B. M., , L. J. Pietrafesa, , D. A. Jay, , and W. C. Boicourt, 1998: The Columbia River Plume Study: Subtidal variability in the velocity and salinity fields. J. Geophys. Res., 103 , (C5). 1033910368.

    • Search Google Scholar
    • Export Citation
  • Hickey, B. M., , S. Geier, , N. Kachel, , and A. MacFadyen, 2005: A bi-directional river plume: The Columbia in summer. Cont. Shelf Res., 25 , 16311656. doi:10.1016/j.csr.2005.04.010.

    • Search Google Scholar
    • Export Citation
  • Hickey, B. M., , R. McCabe, , S. Geier, , E. Dever, , and N. Kachel, 2009: Three interacting freshwater plumes in the northern California Current System. J. Geophys. Res., 114 , C00B03. doi:10.1029/2008JC004907.

    • Search Google Scholar
    • Export Citation
  • Holton, J. R., 1992: An Introduction to Dynamic Meteorology. 3rd ed. Academic Press, 511 pp.

  • Horner-Devine, A. R., 2009: The bulge circulation in the Columbia River plume. Cont. Shelf Res., 29 , 234251. doi:10.1016/j.csr.2007.12.012.

    • Search Google Scholar
    • Export Citation
  • Horner-Devine, A. R., , D. A. Fong, , S. G. Monismith, , and T. Maxworthy, 2006: Laboratory experiments simulating a coastal river inflow. J. Fluid Mech., 555 , 203232. doi:10.1017/S0022112006008937.

    • Search Google Scholar
    • Export Citation
  • Horner-Devine, A. R., , D. A. Jay, , P. M. Orton, , and E. Y. Spahn, 2009: A conceptual model of the strongly tidal Columbia River plume. J. Mar. Syst., 78 , 460475. doi:10.1016/j.jmarsys.2008.11.025.

    • Search Google Scholar
    • Export Citation
  • Kara, A. B., , C. N. Barron, , P. J. Martin, , L. F. Smedstad, , and R. C. Rhodes, 2006: Validation of interannual simulations from the 1/8° global Navy Coastal Ocean Model (NCOM). Ocean Modell., 11 , 376398. doi:10.1016/j.ocemod.2005.01.003.

    • Search Google Scholar
    • Export Citation
  • Kashiwamura, M., , and S. Yoshida, 1967: Outflow pattern of fresh water issued from a river mouth. Coastal Eng. J., 10 , 109115.

  • Lentz, S. J., 2004: The response of buoyant coastal plumes to upwelling-favorable winds. J. Phys. Oceanogr., 34 , 24582469.

  • Li, M., , L. Zhong, , and W. C. Boicourt, 2005: Simulations of Chesapeake Bay estuary: Sensitivity to turbulence mixing parameterizations and comparison with observations. J. Geophys. Res., 110 , C12004. doi:10.1029/2004JC002585.

    • Search Google Scholar
    • Export Citation
  • Liu, W. T., , K. B. Katsaros, , and J. A. Businger, 1979: Bulk parameterization of air-sea exchanges of heat and water vapor including the molecular constraints at the interface. J. Atmos. Sci., 36 , 17221735.

    • Search Google Scholar
    • Export Citation
  • Liu, Y., , P. MacCready, , and B. M. Hickey, 2009a: Columbia River plume patterns in summer 2004 as revealed by a hindcast coastal ocean circulation model. Geophys. Res. Lett., 36 , L02601. doi:10.1029/2008GL036447.

    • Search Google Scholar
    • Export Citation
  • Liu, Y., , P. MacCready, , B. M. Hickey, , E. P. Dever, , P. M. Kosro, , and N. S. Banas, 2009b: Evaluation of a coastal ocean circulation model for the Columbia River plume in summer 2004. J. Geophys. Res., 114 , C00B04. doi:10.1029/2008JC004929.

    • Search Google Scholar
    • Export Citation
  • Lohan, M. C., , and K. W. Bruland, 2006: Importance of vertical mixing for additional sources of nitrate and iron to surface waters of the Columbia River plume: Implications for biology. Mar. Chem., 98 , 260273. doi:10.1016/j.marchem.2005.10.003.

    • Search Google Scholar
    • Export Citation
  • Luketina, D. A., , and J. Imberger, 1987: Characteristics of a surface buoyant jet. J. Geophys. Res., 92 , (C5). 54355447.

  • Luketina, D. A., , and J. Imberger, 1989: Turbulence and entrainment in a buoyant surface plume. J. Geophys. Res., 94 , (C9). 1261912636.

    • Search Google Scholar
    • Export Citation
  • MacCready, P., , N. S. Banas, , B. M. Hickey, , E. P. Dever, , and Y. Liu, 2009: A model study of tide- and wind-induced mixing in the Columbia River estuary and plume. Cont. Shelf Res., 29 , 278291. doi:10.1016/j.csr.2008.03.015.

    • Search Google Scholar
    • Export Citation
  • MacDonald, D. G., , and W. R. Geyer, 2004: Turbulent energy production and entrainment at a highly stratified estuarine front. J. Geophys. Res., 109 , C05004. doi:10.1029/2003JC002094.

    • Search Google Scholar
    • Export Citation
  • MacDonald, D. G., , and W. R. Geyer, 2005: Hydraulic control of a highly stratified estuarine front. J. Phys. Oceanogr., 35 , 374387.

  • MacDonald, D. G., , L. Goodman, , and R. D. Hetland, 2007: Turbulent dissipation in a near-field river plume: A comparison of control volume and microstructure observations with a numerical model. J. Geophys. Res., 112 , C07026. doi:10.1029/2006JC004075.

    • Search Google Scholar
    • Export Citation
  • Marchesiello, P., , J. C. McWilliams, , and A. Shchepetkin, 2001: Open boundary conditions for long-term integration of regional oceanic models. Ocean Modell., 3 , 120.

    • Search Google Scholar
    • Export Citation
  • Marchesiello, P., , J. C. McWilliams, , and A. Shchepetkin, 2003: Equilibrium structure and dynamics of the California Current system. J. Phys. Oceanogr., 33 , 753783.

    • Search Google Scholar
    • Export Citation
  • Mass, C. F., and Coauthors, 2003: Regional environmental prediction over the Pacific Northwest. Bull. Amer. Meteor. Soc., 84 , 13531366.

    • Search Google Scholar
    • Export Citation
  • Masse, A. K., , and C. R. Murthy, 1990: Observations of the Niagara River thermal plume (Lake Ontario, North America). J. Geophys. Res., 95 , (C9). 1609716109.

    • Search Google Scholar
    • Export Citation
  • McCabe, R. M., , B. M. Hickey, , and P. MacCready, 2008: Observational estimates of entrainment and vertical salt flux in the interior of a spreading river plume. J. Geophys. Res., 113 , C08027. doi:10.1029/2007JC004361.

    • Search Google Scholar
    • Export Citation
  • Naik, P. K., , and D. A. Jay, 2005: Estimation of Columbia River virgin flow: 1879 to 1928. Hydrol. Processes, 19 , 18071824. doi:10.1002/hyp.5636.

    • Search Google Scholar
    • Export Citation
  • Nash, J. D., , and J. N. Moum, 2005: River plumes as a source of large-amplitude internal waves in the coastal ocean. Nature, 437 , 400403. doi:10.1038/nature03936.

    • Search Google Scholar
    • Export Citation
  • Nash, J. D., , L. F. Kilcher, , and J. N. Moum, 2009: Structure and composition of a strongly stratified, tidally pulsed river plume. J. Geophys. Res., 114 , C00B12. doi:10.1029/2008JC005036.

    • Search Google Scholar
    • Export Citation
  • O’Donnell, J., , G. O. Marmorino, , and C. L. Trump, 1998: Convergence and downwelling at a river plume front. J. Phys. Oceanogr., 28 , 14811495.

    • Search Google Scholar
    • Export Citation
  • Orton, P. M., , and D. A. Jay, 2005: Observations at the tidal plume front of a high-volume river outflow. Geophys. Res. Lett., 32 , L11605. doi:10.1029/2005GL022372.

    • Search Google Scholar
    • Export Citation
  • Sanders, T. M., , and R. W. Garvine, 2001: Fresh water delivery to the continental shelf and subsequent mixing: An observational study. J. Geophys. Res., 106 , (C11). 2708727101.

    • Search Google Scholar
    • Export Citation
  • Shchepetkin, A. F., , and J. C. McWilliams, 2005: The regional oceanic modeling system (ROMS): A split-explicit, free-surface, topography-following-coordinate oceanic model. Ocean Modell., 9 , 347404. doi:10.1016/j.ocemod.2004.08.002.

    • Search Google Scholar
    • Export Citation
  • Shulman, I., , J. C. Kindle, , S. deRada, , S. C. Anderson, , B. Penta, , and P. J. Martin, 2003: Development of a hierarchy of nested models to study the California Current System. Proc. Eighth Int. Conf. on Estuarine and Coastal Modeling, Monterey, CA, Amer. Soc. Civil Eng., 74–88.

    • Search Google Scholar
    • Export Citation
  • Shulman, I., and Coauthors, 2007: Modeling of upwelling/relaxation events with the Navy Coastal Ocean Model. J. Geophys. Res., 112 , C060623. doi:10.1029/2006JC003946.

    • Search Google Scholar
    • Export Citation
  • Tinis, S. W., , R. E. Thomson, , C. F. Mass, , and B. M. Hickey, 2006: Comparison of MM5 and meteorological buoy winds from British Columbia to Northern California. Atmos.–Ocean, 44 , 6581.

    • Search Google Scholar
    • Export Citation
  • Umlauf, L., , and H. Burchard, 2003: A generic length-scale equation for geophysical turbulence models. J. Mar. Res., 61 , 235265.

  • Vennell, R., 2006: ADCP measurements of momentum balance and dynamic topography in a constricted tidal channel. J. Phys. Oceanogr., 36 , 177188.

    • Search Google Scholar
    • Export Citation
  • Warner, J. C., , W. R. Geyer, , and J. A. Lerczak, 2005a: Numerical modeling of an estuary: A comprehensive skill assessment. J. Geophys. Res., 110 , C05001. doi:10.1029/2004JC002691.

    • Search Google Scholar
    • Export Citation
  • Warner, J. C., , C. R. Sherwood, , H. G. Arango, , and R. P. Signell, 2005b: Performance of four turbulence closure models implemented using a generic length scale method. Ocean Modell., 8 , 81113. doi:10.1016/j.ocemod.2003.12.003.

    • Search Google Scholar
    • Export Citation
  • Whitney, M. M., , and R. W. Garvine, 2005: Wind influence on a coastal buoyant outflow. J. Geophys. Res., 110 , C03014. doi:10.1029/2003JC002261.

    • Search Google Scholar
    • Export Citation
  • Wilkin, J. L., , and W. G. Zhang, 2007: Modes of mesoscale sea surface height and temperature variability in the East Australian Current. J. Geophys. Res., 112 , C01013. doi:10.1029/2006JC003590.

    • Search Google Scholar
    • Export Citation
  • Wright, L. D., , and J. M. Coleman, 1971: Effluent expansion and interfacial mixing in the presence of a salt wedge, Mississippi River Delta. J. Geophys. Res., 76 , 86498661.

    • Search Google Scholar
    • Export Citation
  • Yankovsky, A. E., , and D. C. Chapman, 1997: A simple theory for the fate of buoyant coastal discharges. J. Phys. Oceanogr., 27 , 13861401.

    • Search Google Scholar
    • Export Citation
  • Zhang, W. G., , J. L. Wilkin, , and R. J. Chant, 2009: Modeling the pathways and mean dynamics of river plume dispersal in the New York Bight. J. Phys. Oceanogr., 39 , 11671183.

    • Search Google Scholar
    • Export Citation
Fig. 1.
Fig. 1.

(left) The entire domain of the numerical model, which includes the Washington and northern Oregon shelf and slope and the Columbia River estuary. The resolution of the stretched grid is shown with tick marks at the edges. The Columbia River channel beyond 50 km from the coast is replaced by a straight channel, which absorbs tidal energy. Bathymetry contour intervals are 100 (thin lines) and 500 m (thick lines). The two bays north of the Columbia River mouth are Willapa Bay and Grays Harbor. (right) A close-up of the gray region in (left). Here, thin lines show isobaths on the shelf at 50-m intervals, and the grid resolution is ∼400 m.

Citation: Journal of Physical Oceanography 39, 11; 10.1175/2009JPO4061.1

Fig. 2.
Fig. 2.

A time series of 9 Jun 2005 tidal conditions at the Columbia River mouth (46.2542°N, 124.0833°W) from the model. Model surface elevation η (m) is represented by the thick black line and model surface currents U (m s−1) are represented by the thick gray line. Negative (positive) currents ebb (flood) out (into) the estuary. Three different times have been chosen to represent the greater ebb: near maximum ebb (before tidal currents significantly relax), midebb, and just after slack conditions.

Citation: Journal of Physical Oceanography 39, 11; 10.1175/2009JPO4061.1

Fig. 3.
Fig. 3.

(a) A comparison between observed surface drifter tracks (four thick gray lines) from an experiment on 9 Jun 2005 (see McCabe et al. 2008) and numerical surface floats (tracks colored by salinity) from a realistic ROMS hindcast. Field drifters were released on a greater ebb, near the time of maximum ebb currents. Model floats pass the field drifter release locations within ∼10 min of the field deployment times. All tracks are 8 h long. Bathymetric contours (thin gray lines) are drawn at 10-, 20-, 50-, 100-, 200-, and 500-m depths. The time series of mean observed and numerical float (b) salinities and (c) speeds show plume dilution and flow deceleration.

Citation: Journal of Physical Oceanography 39, 11; 10.1175/2009JPO4061.1

Fig. 4.
Fig. 4.

Model flow properties (∼30-min average) in the near-field region of the Columbia River plume, near the time of maximum ebb currents. (b),(d)–(o) Surface plan view (lat, lon). (a) Tidal height and surface currents from Fig. 2, showing timing with respect to tidal phase and averaging duration (vertical gray band); (b) a plan view of the surface salinity S with bathymetry contours at 10-, 20-, 50-, 100-, 200-, and 500-m depths in black; (c) a vertical section of salinity (S = 26, drawn black) along the dashed white line in (b); (d) sea surface height anomaly Δη (cm) relative to a nearshore value outside of buoyant plume water, with bathymetry contours as in (b); and (e) surface velocity vectors showing the ebb momentum pulse. Contributions to the surface streamwise momentum balance (m s−2): (f) local acceleration, the first term in Eq. (1); (g) total advective acceleration, which is the sum of the second and third terms in Eq. (1); (h) the streamwise pressure gradient field, which is the fourth term in Eq. (1); (i) Coriolis acceleration, which is zero by definition; and (j) the streamwise vertical stress divergence, which is the sum of the fifth and sixth terms in Eq. (1). Contributors to the surface stream-normal momentum balance (m s−2): (k) rotary acceleration, which is the first term in Eq. (2); (l) stream-normal advective acceleration, which is the sum of the second and third terms in Eq. (2) (primarily centrifugal near the surface); (m) the stream-normal pressure gradient, which is the fifth term in Eq. (2); (n) Coriolis acceleration, which is the fourth term in Eq. (2); and (o) stream-normal vertical stress divergence, which is the sum of the sixth and seventh terms in Eq. (2).

Citation: Journal of Physical Oceanography 39, 11; 10.1175/2009JPO4061.1

Fig. 5.
Fig. 5.

As in Fig. 4, but for midebb. Seven surface float tracks (gray lines) are also shown in all plan-view panels. Black dots mark the current float positions. Floats were released across the river mouth at the time of Fig. 4 (maximum ebb) and have therefore traveled for ∼2.5 h.

Citation: Journal of Physical Oceanography 39, 11; 10.1175/2009JPO4061.1

Fig. 6.
Fig. 6.

As in Fig. 4, but near slack conditions. Seven surface float tracks (gray lines) are also shown in all plan-view panels. Black dots mark the current float positions. Floats were released across the river mouth at the time of Fig. 4 (maximum ebb) and have therefore traveled for ∼4.5 h.

Citation: Journal of Physical Oceanography 39, 11; 10.1175/2009JPO4061.1

Fig. 7.
Fig. 7.

(a) A plan view of the model surface salinity near the time of slack conditions (as in Fig. 6b), including the seven surface float tracks (gray). Current float positions are denoted with black dots. Three float tracks (north, central, and south) are highlighted magenta. Streamwise–normal momentum contributions following the highlighted float tracks are included: (b) north, (c) central, and (d) south. Color-coded momentum equations are also included as a legend for identifying specific momentum terms. The naming convention is consistent with Figs. 4 –6. Temporal derivatives are dotted black lines, advective terms are red lines, pressure gradient terms are green lines, friction terms are blue lines, and the Coriolis accelerations are solid black lines.

Citation: Journal of Physical Oceanography 39, 11; 10.1175/2009JPO4061.1

Fig. 8.
Fig. 8.

Vertical sections of (a) salinity, (b) streamwise vertical shear (s−1) calculated relative to the surface flow direction, (c) stress (10−4 m2 s−2) with surface wind stress appended at the top, and (d) vertical salt flux (10−3 m s−1) through the outflowing plume at midebb (i.e., the time of Fig. 5). The negative values in (c) are in a region of up-estuary flow (to the right). Each section was taken along the transect shown in Fig. 5b and was averaged over ∼31 min. For reference, the isohaline with salinity 26 is drawn as black lines. The largest vertical momentum and salt fluxes in the plume occur at lift-off. However, much also occurs in the plume interior at midplume depths where stratification and vertical shear are large.

Citation: Journal of Physical Oceanography 39, 11; 10.1175/2009JPO4061.1

Fig. 9.
Fig. 9.

Plume spreading as measured with a pair of surface-trapped horizontal Lagrangian drifters. Two adjacent drifters are at positions r1(t) and r2(t) at time t. The drifters have instantaneous velocity vectors U1(t) and U2(t), with local streamline angles α1 and α2. Drifter separation is given by B = r2(t) − r1(t), and the spreading rate following the drifters is dU = U2(t) − U1(t) = DB/Dt.

Citation: Journal of Physical Oceanography 39, 11; 10.1175/2009JPO4061.1

Fig. 10.
Fig. 10.

The distance (km) between adjacent model floats (B; thick black line) in Fig. 7a for the last half of the ebb cycle. Floats were released near the time of maximum ebb currents (at the time of Fig. 4). Also included are the portions of float spreading that result from differences in adjacent float streamwise velocities [BU); thick gray line] and from differences in adjacent float directions [Bα); thin black line].

Citation: Journal of Physical Oceanography 39, 11; 10.1175/2009JPO4061.1

Fig. 11.
Fig. 11.

Cumulative along-track integrals of the Coriolis (thick black line), cross-stream pressure gradient (thick gray line), and cross-stream frictional stress (dashed gray line) terms of the normal-direction momentum equation following numerical floats, and their sum (dashed black line) as a function of time. Floats are selected from the (a) north side, (b) center, and (c) south side of the plume.

Citation: Journal of Physical Oceanography 39, 11; 10.1175/2009JPO4061.1

* RISE Contribution Number 30.

Save