• Banas, N. S., B. M. Hickey, P. MacCready, and J. A. Newton, 2004: Dynamics of Willapa Bay, Washington: A highly unsteady, partially mixed estuary. J. Phys. Oceanogr., 34, 24132427.

    • Search Google Scholar
    • Export Citation
  • Blumberg, A. F., and G. L. Mellor, 1987: A description of a three-dimensional coastal ocean circulation model. Three-Dimensional Coastal Ocean Models, N. S. Heaps, Ed., Coastal Estuarine Sciences, Vol. 4, Amer. Geophys. Union, 1–16.

  • Burchard, H., and H. Baumert, 1998: The formation of estuarine turbidity maxima due to density effects in the salt wedge. A hydrodynamic process study. J. Phys. Oceanogr., 28, 309321.

    • Search Google Scholar
    • Export Citation
  • Burchard, H., and R. D. Hetland, 2010: Quantifying the contributions of tidal straining and gravitational circulation to residual circulation in periodically stratified tidal estuaries. J. Phys. Oceanogr., 40, 12431262.

    • Search Google Scholar
    • Export Citation
  • Chant, R. J., and R. E. Wilson, 1997: Secondary circulation in a highly stratified estuary. J. Geophys. Res., 102 (C10), 23 20723 215.

    • Search Google Scholar
    • Export Citation
  • Chen, S., W. R. Geyer, D. K. Ralston, and J. A. Lerczak, 2012: Estuarine exchange flow quantified with isohaline coordinates: Contrasting long and short estuaries. J. Phys. Oceanogr., 42, 748763.

    • Search Google Scholar
    • Export Citation
  • Chickadel, C. C., A. R. Horner-Devine, S. A. Talke, and A. T. Jessup, 2009: Vertical boil propagation from a submerged estuarine sill. Geophys. Res. Lett., 36, L10601, doi:10.1029/2009GL037278.

    • Search Google Scholar
    • Export Citation
  • Dronkers, J., and J. van de Kreeke, 1986: Experimental determination of salt intrusion mechanisms in the Volkerak estuary. Neth. J. Sea Res., 20, 119, doi:10.1016/0077-7579(86)90056-6.

    • Search Google Scholar
    • Export Citation
  • Emery, W. J., and R. E. Thomson, 2004: Data Analysis Methods in Physical Oceanography. 2nd ed. Elsevier, 638 pp.

  • Fischer, H. B., E. J. List, R. C. Y. Koh, J. Imberger, and N. H. Brooks, 1979: Mixing in Inland and Coastal Waters. Academic Press, Inc., 302 pp.

  • Geyer, W. R., and H. Nepf, 1996: Tidal pumping of salt in a moderately stratified estuary. Coastal Estuarine Stud., 53, 213226.

  • Geyer, W. R., J. H. Trowbridge, and M. M. Bowen, 2000: The dynamics of a partially mixed estuary. J. Phys. Oceanogr., 30, 11 62911 637.

    • Search Google Scholar
    • Export Citation
  • Geyer, W. R., M. E. Scully, and D. K. Ralston, 2008: Quantifying vertical mixing in estuaries. Environ. Fluid Mech., 8, 495509.

  • Giddings, S. N., D. A. Fong, and S. G. Monismith, 2011: Role of straining and advection in the intratidal evolution of stratification, vertical mixing, and longitudinal dispersion of a shallow, macrotidal, salt wedge estuary. J. Geophys. Res., 116, C03003, doi:10.1029/2010JC006482.

    • Search Google Scholar
    • Export Citation
  • Giddings, S. N., and Coauthors, 2012: Frontogenesis and frontal progression of a trapping-generated estuarine convergence front and its influence on mixing and stratification. Estuaries Coasts, 35, 665681, doi:10.1007/s12237-011-9453-z.

    • Search Google Scholar
    • Export Citation
  • Godin, G., 1995: Magnitude of Stokes' drift in coastal waters. Ocean Dyn., 47, 277286, doi:10.1007/BF02737788.

  • Hamrick, J. M., 1990: The dynamics of long-term mass transport in estuaries. Coastal Estuarine Stud., 38, 1733.

  • Hansen, D. V., and M. Rattray Jr., 1965: Gravitational circulation in straits and estuaries. J. Mar. Res., 23, 104122.

  • Hetland, R. D., and W. R. Geyer, 2004: An idealized study of the structure of long, partially mixed estuaries. J. Phys. Oceanogr., 34, 26772691.

    • Search Google Scholar
    • Export Citation
  • Ianniello, J. P., 1979: Tidally induced residual currents in estuaries of variable breadth and depth. J. Phys. Oceanogr., 9, 962974.

  • Jay, D. A., and J. D. Smith, 1990: Residual circulation in shallow estuaries: 1. Highly stratified, narrow estuaries. J. Geophys. Res., 95 (C1), 711731.

    • Search Google Scholar
    • Export Citation
  • Jay, D. A., and J. D. Musiak, 1994: Particle trapping in estuarine tidal flows. J. Geophys. Res., 99 (C10), 20 44520 461.

  • Jay, D. A., and J. D. Musiak, 1996: Internal tidal asymmetry in channel flows: Origins and consequences. Mixing Processes in Estuaries and Coastal Seas, C. B. Pattiaratchi, Ed., Coastal and Estuarine Studies Series, Vol. 50, Amer. Geophys. Union, 211–249.

  • Kjerfve, B., 1975: Velocity averaging in estuaries characterized by a large tidal range to depth ratio. Estuarine Coastal Mar. Sci., 3, 311–323.

    • Search Google Scholar
    • Export Citation
  • Kranenburg, C., 1986: A time scale for long-term salt intrusion in well-mixed estuaries. J. Phys. Oceanogr., 16, 13291331.

  • Kuo, A. Y., J. M. Hamrick, and G. M. Sisson, 1990: Persistence of residual currents in the James River estuary and its implication to mass transport. Coastal Estuarine Stud., 38, 389401.

    • Search Google Scholar
    • Export Citation
  • Lacy, J. R., M. T. Stacey, J. R. Burau, and S. G. Monismith, 2003: Interaction of lateral baroclinic forcing and turbulence in an estuary. J. Geophys. Res., 108, 3089, doi:10.1029/2002JC001392.

    • Search Google Scholar
    • Export Citation
  • Lerczak, J. A., and W. R. Geyer, 2004: Modeling the lateral circulation in straight, stratified estuaries. J. Phys. Oceanogr., 34, 14101428.

    • Search Google Scholar
    • Export Citation
  • Lerczak, J. A., W. R. Geyer, and R. J. Chant, 2006: Mechanisms driving the time-dependent salt flux in a partially stratified estuary. J. Phys. Oceanogr., 36, 22962311.

    • Search Google Scholar
    • Export Citation
  • Li, C., and J. O'Donnell, 1997: Tidally driven residual circulation in shallow estuaries with lateral depth variation. J. Geophys. Res., 102 (C13), 27 91527 929.

    • Search Google Scholar
    • Export Citation
  • Longuet-Higgins, M. S., 1969: On the transport of mass by time-varying ocean currents. Deep Sea Res. Oceanogr. Abstr., 16, 431447, doi:10.1016/0011-7471(69)90031-X.

    • Search Google Scholar
    • Export Citation
  • Lu, Y., and R. G. Lueck, 1999: Using a broadband ADCP in a tidal channel. Part II: Turbulence. J. Atmos. Oceanic Technol., 16, 15681579.

    • Search Google Scholar
    • Export Citation
  • MacCready, P., 2004: Toward a unified theory of tidally-averaged estuarine salinity structure. Estuaries, 27, 561570.

  • MacCready, P., 2011: Calculating estuarine exchange flow using isohaline coordinates. J. Phys. Oceanogr., 41, 11161124.

  • MacCready, P., and W. R. Geyer, 2010: Advances in estuarine physics. Annu. Rev. Mar. Sci., 2, 3558, doi:10.1146/annurev-marine-120308-081015.

    • Search Google Scholar
    • Export Citation
  • MacDonald, D. G., and A. R. Horner-Devine, 2008: Temporal and spatial variability of vertical salt flux in a highly stratified estuary. J. Geophys. Res., 113, C09022, doi:10.1029/2007JC004620.

    • Search Google Scholar
    • Export Citation
  • Monismith, S. G., J. R. Burau, and M. T. Stacey, 1996: Stratification dynamics and gravitational circulation in northern San Francisco Bay. San Francisco Bay: The Ecosystem, T. Hollibaugh, Ed., AAAS, 123–153.

  • Monismith, S. G., W. Kimmerer, J. R. Burau, and M. T. Stacey, 2002: Structure and flow-induced variability of the subtidal salinity field in northern San Francisco Bay. J. Phys. Oceanogr., 32, 30033019.

    • Search Google Scholar
    • Export Citation
  • Nidzieko, N. J., D. A. Fong, and J. L. Hench, 2006: Comparison of Reynolds stress estimates derived from standard and fast-ping ADCPs. J. Atmos. Oceanic Technol., 23, 854861.

    • Search Google Scholar
    • Export Citation
  • Plant, W. J., and Coauthors, 2009: Remotely sensed river surface features compared with modeling and in situ measurements. J. Geophys. Res., 114, C11002, doi:10.1029/2009JC005440.

    • Search Google Scholar
    • Export Citation
  • Prandle, D., 2004: Saline intrusion in partially mixed estuaries. Estuarine Coastal Shelf Sci., 59, 385–397.

  • Pritchard, D. W., 1954: A study of the salt balance in a coastal plain estuary. J. Mar. Res., 13, 133144.

  • Pritchard, D. W., 1956: The dynamics structure of a coastal plain estuary. J. Mar. Res., 15, 3342.

  • Ralston, D. K., W. R. Geyer, and J. A. Lerczak, 2010: Structure, variability, and salt flux in a strongly forced salt wedge estuary. J. Geophys. Res., 115, C06005, doi:10.1029/2009JC005806.

    • Search Google Scholar
    • Export Citation
  • Rattray, M., Jr., and J. G. Dworski, 1980: Comparison of methods for analysis of the transverse and vertical circulation contributions to the longitudinal advective salt flux in estuaries. Estuarine Coastal Mar. Sci., 11, 515536.

    • Search Google Scholar
    • Export Citation
  • Scully, M. E., and C. T. Friedrichs, 2007: The importance of tidal and lateral asymmetries in stratification to residual circulation in partially mixed estuaries. J. Phys. Oceanogr., 37, 14961511.

    • Search Google Scholar
    • Export Citation
  • Scully, M. E., W. R. Geyer, and J. A. Lerczak, 2009: The influence of lateral advection on the residual estuarine circulation: A numerical modeling study of the Hudson River estuary. J. Phys. Oceanogr., 39, 107–124.

    • Search Google Scholar
    • Export Citation
  • Simpson, J. H., J. Brown, J. Matthews, and G. Allen, 1990: Tidal straining, density currents, and stirring in the control of estuarine stratification. Estuaries, 13, 125132.

    • Search Google Scholar
    • Export Citation
  • Stacey, M. T., S. G. Monismith, and J. R. Burau, 1999: Measurements of Reynolds stress profiles in unstratified tidal flow. J. Geophys. Res., 104 (C5), 10 93310 949, doi:10.1029/1998JC900095.

    • Search Google Scholar
    • Export Citation
  • Stacey, M. T., J. R. Burau, and S. G. Monismith, 2001: Creation of residual flows in a partially stratified estuary. J. Geophys. Res., 106 (C8), 17 01317 037.

    • Search Google Scholar
    • Export Citation
  • Stacey, M. T., M. L. Brennan, J. R. Burau, and S. G. Monismith, 2010: The tidally averaged momentum balance in a partially and periodically stratified estuary. J. Phys. Oceanogr., 40, 24182434.

    • Search Google Scholar
    • Export Citation
  • Tedford, E. W., J. R. Carpenter, R. Pawlowicz, R. Pieters, and G. A. Lawrence, 2009: Observation and analysis of shear instability in the Fraser River estuary. J. Geophys. Res., 114, C11006, doi:10.1029/2009JC005313.

    • Search Google Scholar
    • Export Citation
  • Trowbridge, J. H., W. R. Geyer, M. M. Bowen, and A. J. Williams III, 1999: Near-bottom turbulence measurements in a partially mixed estuary: Turbulent energy balance, velocity structure, and along-channel momentum balance. J. Phys. Oceanogr., 29, 30563072.

    • Search Google Scholar
    • Export Citation
  • Uncles, R. J., 2002: Estuarine physical processes research: Some recent studies and progress. Estuarine Coastal Shelf Sci., 55, 829856.

    • Search Google Scholar
    • Export Citation
  • Uncles, R. J., and M. B. Jordan, 1980: A one-dimensional representation of residual currents in the Severn estuary and associated observations. Estuarine Coastal Mar. Sci., 10, 3960, doi:10.1016/S0302-3524(80)80048-X.

    • Search Google Scholar
    • Export Citation
  • Uncles, R. J., and J. A. Stephens, 1990: The structure of vertical current profiles in a macrotidal, partly-mixed estuary. Estuaries, 13, 349361.

    • Search Google Scholar
    • Export Citation
  • Uncles, R. J., R. C. A. Elliott, and S. A. Weston, 1985: Observed fluxes of water, salt and suspended sediment in a partly mixed estuary. Estuarine Coastal Shelf Sci., 20, 147167, doi:10.1016/0272-7714(85)90035-6.

    • Search Google Scholar
    • Export Citation
  • Valle-Levinson, A., C. Li, K.-C. Wong, and K. M. M. Lwiza, 2000: Convergence of lateral flow along a coastal plain estuary. J. Geophys. Res., 105 (C7), 17 04517 061, doi:10.1029/2000JC900025.

    • Search Google Scholar
    • Export Citation
  • van de Kreeke, J., and A. A. Chiu, 1981: Tide-induced residual flow in shallow bays. J. Hydraul. Res., 19, 231249, doi:10.1080/00221688109499517.

    • Search Google Scholar
    • Export Citation
  • Wang, B., O. B. Fringer, S. N. Giddings, and D. A. Fong, 2009: High-resolution simulations of a macrotidal estuary using SUNTANS. Ocean Modell., 26, 6085, doi:10.1016/j.ocemod.2008.08.006.

    • Search Google Scholar
    • Export Citation
  • Wang, B., S. N. Giddings, O. B. Fringer, E. S. Gross, D. A. Fong, and S. G. Monismith, 2011: Modeling and understanding turbulent mixing in a macrotidal salt wedge estuary. J. Geophys. Res., 116, C02036, doi:10.1029/2010JC006135.

    • Search Google Scholar
    • Export Citation
  • West, J. R., R. J. Uncles, J. A. Stephens, and K. Shiono, 1990: Longitudinal dispersion processes in the Upper Tamar estuary. Estuaries, 13, 118–124.

    • Search Google Scholar
    • Export Citation
  • Williams, E., and J. H. Simpson, 2004: Uncertainties in estimates of Reynolds stress and TKE production rate using the ADCP variance method. J. Atmos. Oceanic Technol., 21, 347–357.

    • Search Google Scholar
    • Export Citation
  • Zimmerman, J. T. F., 1979: On the Euler-Lagrange transformation and the Stokes' drift in the presence of oscillatory and residual currents. Deep-Sea Res., 26, 505520, doi:10.1016/0198-0149(79)90093-1.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 300 113 4
PDF Downloads 168 68 3

Using Depth-Normalized Coordinates to Examine Mass Transport Residual Circulation in Estuaries with Large Tidal Amplitude Relative to the Mean Depth

View More View Less
  • 1 School of Oceanography, University of Washington, Seattle, Washington
  • | 2 Environmental Fluid Mechanics Laboratory, Department of Civil and Environmental Engineering, Stanford University, Stanford, California
  • | 3 Department of Civil and Environmental Engineering, University of California, Berkeley, Berkeley, California
Restricted access

Abstract

Residual (subtidal) circulation profiles in estuaries with a large tidal amplitude-to-depth ratio often are quite complex and do not resemble the traditional estuarine gravitational circulation profile. This paper describes how a depth-normalized σ-coordinate system allows for a more physical interpretation of residual circulation profiles than does a fixed vertical coordinate system in an estuary with a tidal amplitude comparable to the mean depth. Depth-normalized coordinates permit the approximation of Lagrangian residuals, performance of empirical orthogonal function (EOF) analysis, estimation of terms in the along-stream momentum equations throughout depth, and computation of a tidally averaged momentum balance. The residual mass transport velocity has an enhanced two-layer exchange flow relative to an Eulerian mean because of the Stokes wave transport velocity directed upstream at all depths. While the observed σ-coordinate profiles resemble gravitational circulation, and pressure and friction are the dominant terms in the tidally varying and tidally averaged momentum equations, the two-layer shear velocity from an EOF analysis does not correlate with the along-stream density gradient. To directly compare to theoretical profiles, an extension of a pressure–friction balance in σ coordinates is solved. While the barotropic riverine residual matches theory, the mean longitudinal density gradient and mean vertical mixing cannot explain the magnitude of the observed two-layer shear residual. In addition, residual shear circulation in this system is strongly driven by asymmetries during the tidal cycle, particularly straining and advection of the salinity field, creating intratidal variation in stratification, vertical mixing, and shear.

Now at Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California.

Corresponding author address: Sarah N. Giddings, University of California, San Diego, 9500 Gilman Dr. #0206, La Jolla, CA 92093-0206. E-mail: sarahgid@ucsd.edu

Abstract

Residual (subtidal) circulation profiles in estuaries with a large tidal amplitude-to-depth ratio often are quite complex and do not resemble the traditional estuarine gravitational circulation profile. This paper describes how a depth-normalized σ-coordinate system allows for a more physical interpretation of residual circulation profiles than does a fixed vertical coordinate system in an estuary with a tidal amplitude comparable to the mean depth. Depth-normalized coordinates permit the approximation of Lagrangian residuals, performance of empirical orthogonal function (EOF) analysis, estimation of terms in the along-stream momentum equations throughout depth, and computation of a tidally averaged momentum balance. The residual mass transport velocity has an enhanced two-layer exchange flow relative to an Eulerian mean because of the Stokes wave transport velocity directed upstream at all depths. While the observed σ-coordinate profiles resemble gravitational circulation, and pressure and friction are the dominant terms in the tidally varying and tidally averaged momentum equations, the two-layer shear velocity from an EOF analysis does not correlate with the along-stream density gradient. To directly compare to theoretical profiles, an extension of a pressure–friction balance in σ coordinates is solved. While the barotropic riverine residual matches theory, the mean longitudinal density gradient and mean vertical mixing cannot explain the magnitude of the observed two-layer shear residual. In addition, residual shear circulation in this system is strongly driven by asymmetries during the tidal cycle, particularly straining and advection of the salinity field, creating intratidal variation in stratification, vertical mixing, and shear.

Now at Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California.

Corresponding author address: Sarah N. Giddings, University of California, San Diego, 9500 Gilman Dr. #0206, La Jolla, CA 92093-0206. E-mail: sarahgid@ucsd.edu
Save