• Alford, M. H., 2003: Redistribution of energy available for ocean mixing by long-range propagation of internal waves. Nature, 423, 159162.

    • Search Google Scholar
    • Export Citation
  • Alford, M. H., 2010: Sustained, full-water-column observations of internal waves and mixing near Mendocino Escarpment. J. Phys. Oceanogr., 40, 26432660.

    • Search Google Scholar
    • Export Citation
  • Alford, M. H., , and Z. Zhao, 2007a: Global patterns of low-mode internal-wave propagation. Part I: Energy and energy flux. J. Phys. Oceanogr., 37, 18291848.

    • Search Google Scholar
    • Export Citation
  • Alford, M. H., , and Z. Zhao, 2007b: Global patterns of low-mode internal-wave propagation. Part II: Group velocity. J. Phys. Oceanogr., 37, 18491858.

    • Search Google Scholar
    • Export Citation
  • Alford, M. H., , M. C. Gregg, , and M. A. Merrifield, 2006: Structure, propagation and mixing of energetic baronlinic tides in Mamala Bay, Oahu, Hawaii. J. Phys. Oceanogr., 36, 9971018.

    • Search Google Scholar
    • Export Citation
  • Alford, M. H., and Coauthors, 2011: Energy flux and dissipation in Luzon Strait: Two tales of two ridges. J. Phys. Oceanogr., 41, 22112222.

    • Search Google Scholar
    • Export Citation
  • Buijsman, M. C., , S. Legg, , and J. Klymak, 2012: Double-ridge internal tide interference and its effect on dissipation in Luzon Strait. J. Phys. Oceanogr., 42, 13371356.

    • Search Google Scholar
    • Export Citation
  • Cairns, J. L., , and G. O. Williams, 1976: Internal wave observations from a midwater float, 2. J. Geophys. Res., 81, 19431950.

  • Carter, G. S., 2010: Barotropic and baroclinic M2 tides in the Monterey Bay region. J. Phys. Oceanogr., 40, 17661783.

  • Carter, G. S., , and M. C. Gregg, 2002: Intense, variable mixing near the head of Monterey submarine canyon. J. Phys. Oceanogr., 32, 31453165.

    • Search Google Scholar
    • Export Citation
  • Carter, G. S., , M. C. Gregg, , and R.-C. Lien, 2005: Internal waves, solitary-like waves, and mixing on the Monterey Bay shelf. Cont. Shelf Res., 25, 14991520.

    • Search Google Scholar
    • Export Citation
  • Dale, A. C., , J. M. Huthnance, , and T. J. Sherwin, 2001: Coastal-trapped waves and tides at near-inertial frequencies. J. Phys. Oceanogr., 31, 29582970.

    • Search Google Scholar
    • Export Citation
  • Dillon, T. M., 1982: Vertical overturns: A comparison of Thorpe and Ozmidov length scales. J. Geophys. Res., 87, 96019613.

  • Doherty, K. W., , D. E. Frye, , S. P. Liberatore, , and J. M. Toole, 1999: A moored profiling instrument. J. Atmos. Oceanic Technol., 16, 18161829.

    • Search Google Scholar
    • Export Citation
  • Eriksen, C. C., 1982: Observations of internal wave reflection off sloping bottoms. J. Geophys. Res., 87, 525538.

  • Galbraith, P. S., , and D. E. Kelley, 1996: Identifying overturns in CTD profiles. J. Atmos. Oceanic Technol., 13, 688702.

  • Gardner, W. D., 1989: Periodic resuspension in Baltimore Canyon by focusing of internal waves. J. Geophys. Res., 94, 18 18518 194.

  • Garrett, C., , and W. H. Munk, 1975: Space-time scales of internal waves: A progress report. J. Geophys. Res., 80, 291297.

  • Gill, A. E., 1982: Atmosphere-Ocean Dynamics. Academic Press, 662 pp.

  • Gonella, J., 1972: A rotary-component method for analysing meteorological and oceanographic vector time series. Deep-Sea Res., 19, 833846, doi:10.1016/0011-7471(72)90002-2.

    • Search Google Scholar
    • Export Citation
  • Gordon, R. L., , and N. F. Marshall, 1976: Submarine canyon internal wave traps? Geophys. Res. Lett., 3, 622624.

  • Gregg, M. C., , G. S. Carter, , and E. Kunze, 2005: Corrigendum. J. Phys. Oceanogr., 35, 17121715.

  • Gregg, M. C., , R. A. Hall, , G. S. Carter, , M. H. Alford, , R.-C. Lien, , D. P. Winkel, , and D. J. Wain, 2011: Flow and mixing in Ascension, a steep, narrow canyon. J. Geophys. Res.,116, C07016, doi:10.1029/2010JC006610.

  • Hall, P., , and A. M. Davies, 2007: Internal tide modeling and the influence of wind effects. Cont. Shelf Res., 27, 13571377, doi:10.1016/j.csr.2006.09.008.

    • Search Google Scholar
    • Export Citation
  • Hall, R. A., , and G. S. Carter, 2011: Internal tides in Monterey Submarine Canyon. J. Phys. Oceanogr., 41, 186204.

  • Hickey, B. M., 1995: Coastal submarine canyons. Topographic Interactions in the Ocean: Proc. ‘Aha Huliko‘a Hawaiian Winter Workshop, Honolulu, HI, University of Hawaii at Manoa, 95–110.

  • Hotchkiss, F. S., , and C. Wunsch, 1982: Internal waves in Hudson Canyon with possible geological implications. Deep-Sea Res., 29, 415442.

    • Search Google Scholar
    • Export Citation
  • Hunkins, K., 1988: Mean and tidal currents in Baltimore Canyon. J. Geophys. Res., 93, 69176929.

  • Jachec, S. M., , O. B. Fringer, , M. G. Gerritsen, , and R. L. Street, 2006: Numerical simulation of internal tides and the resulting energetics within Monterey Bay and the surrounding area. Geophys. Res. Lett.,33, L12605, doi:10.1029/2006GL026314.

  • Johnston, T. M. S., , D. L. Rudnick, , G. S. Carter, , R. E. Todd, , and S. T. Cole, 2011: Internal tidal beams and mixing near Monterey Bay. J. Geophys. Res., 116, C03017, doi:10.1029/2010JC006592.

    • Search Google Scholar
    • Export Citation
  • Kang, D., , and O. B. Fringer, 2012: Energetics of barotropic and baroclinic tides in the Monterey Bay area. J. Phys. Oceanogr., 42, 272290.

    • Search Google Scholar
    • Export Citation
  • Kelly, S. M., , and J. D. Nash, 2010: Internal-tide generation and destruction by shoaling internal tides. Geophys. Res. Lett., 37, L23611, doi:10.1029/2010GL045598.

    • Search Google Scholar
    • Export Citation
  • Kelly, S. M., , J. D. Nash, , M. H. Alford, , and K. I. Martini, 2012: The cascade of tidal energy from low to high modes on a continental slope. J. Phys. Oceanogr., 42, 12171232.

    • Search Google Scholar
    • Export Citation
  • Key, S. A., 1999: Internal tidal bores in the Monterey Canyon. M.S. thesis, Department of Oceanography, Naval Postgraduate School, 91 pp.

  • Klymak, J. M., , M. H. Alford, , R. Pinkel, , R.-C. Lien, , Y. J. Yang, , and T.-Y. Tang, 2011: The breaking and scattering of the internal tide on a continental slope. J. Phys. Oceanogr., 41, 926945.

    • Search Google Scholar
    • Export Citation
  • Kunze, E., , L. K. Rosenfeld, , G. S. Carter, , and M. C. Gregg, 2002: Internal waves in Monterey submarine canyon. J. Phys. Oceanogr., 32, 18901913.

    • Search Google Scholar
    • Export Citation
  • Kunze, E., , C. MacKay, , E. E. McPhee-Shaw, , K. Morrice, , J. B. Girton, , and S. R. Terker, 2012: Turbulent mixing and exchange with interior waters on sloping boundaries. J. Phys. Oceanogr., 42, 910–927.

    • Search Google Scholar
    • Export Citation
  • Kurapov, A. L., , G. D. Egbert, , J. S. Allen, , R. N. Miller, , S. Y. Erofeeva, , and P. M. Kosro, 2003: The M2 internal tide off Oregon: Inferences from data assimilation. J. Phys. Oceanogr., 33, 17331757.

    • Search Google Scholar
    • Export Citation
  • Kurapov, A. L., , J. S. Allen, , and G. D. Egbert, 2010: Combined effects of wind-driven upwelling and internal tide on the continental shelf. J. Phys. Oceanogr., 40, 737756.

    • Search Google Scholar
    • Export Citation
  • Lee, I.-H., , R.-C. Lien, , J. T. Liu, , and W.-S. Chuang, 2009: Turbulent mixing and internal tides in Gaoping (Kaoping) Submarine Canyon, Taiwan. J. Mar. Syst., 76, 383396, doi:10.1016/j.jmarsys.2007.08.005.

    • Search Google Scholar
    • Export Citation
  • Legg, S., , and J. Klymak, 2008: Internal hydraulic jumps and overturning generated by tidal flow over a tall steep ridge. J. Phys. Oceanogr., 38, 19491964.

    • Search Google Scholar
    • Export Citation
  • Lueck, R. G., , and T. R. Osborn, 1985: Turbulence measurements in a submarine canyon. Cont. Shelf Res., 4, 681698.

  • MacKinnon, J. A., , and M. C. Gregg, 2003a: Mixing on the late-summer New England shelf–solibores, shear and stratification. J. Phys. Oceanogr., 33, 14761492.

    • Search Google Scholar
    • Export Citation
  • MacKinnon, J. A., , and M. C. Gregg, 2003b: Shear and baroclinic energy flux on the summer New England shelf. J. Phys. Oceanogr., 33, 14621475.

    • Search Google Scholar
    • Export Citation
  • Martini, K. I., , M. H. Alford, , J. D. Nash, , E. Kunze, , and M. A. Merrifield, 2007: Diagnosing a partly-standing internal wave in Mamala Bay, Oahu. Geophys. Res. Lett.,34, L17604, doi:10.1029/2007GL029749.

  • Mooers, C. N. K., 1970: The interaction of an internal tide with the frontal zone in a coastal upwelling region. Ph.D. thesis, Oregon State University, 480 pp.

  • Nash, J. D., , E. Kunze, , J. M. Toole, , and R. W. Schmitt, 2004: Internal tide reflection and turbulent mixing on the continental slope. J. Phys. Oceanogr., 34, 11171134.

    • Search Google Scholar
    • Export Citation
  • Nash, J. D., , M. H. Alford, , and E. Kunze, 2005: Estimating internal wave energy fluxes in the ocean. J. Atmos. Oceanic Technol., 22, 15511570.

    • Search Google Scholar
    • Export Citation
  • Osborne, J. J., , A. L. Kurapov, , G. D. Egbert, , and P. M. Kosro, 2011: Spatial and temporal variability of the M2 internal tide generation and propagation on the Oregon shelf. J. Phys. Oceanogr., 41, 20372062.

    • Search Google Scholar
    • Export Citation
  • Paduan, J. D., , and L. K. Rosenfeld, 1996: Remotely sensed surface currents in Monterey Bay from shore-based HF radar (coastal ocean dynamics application radar). J. Geophys. Res., 101 (C9), 20 66920 686.

    • Search Google Scholar
    • Export Citation
  • Paull, C. K., , P. Mitts, , W. Ussler III, , R. Keaten, , and H. G. Greene, 2005: Trail of sand in upper Monterey Canyon: Offshore California. Geol. Soc. Amer. Bull., 117, 11341145, doi:10.1130/B25390.1.

    • Search Google Scholar
    • Export Citation
  • Pawlowicz, R., , B. Beardsley, , and S. Lentz, 2002: Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE. Comput. Geosci., 28, 929937.

    • Search Google Scholar
    • Export Citation
  • Pedlosky, J., 2003: Waves in the Ocean and Atmosphere: Introduction to Wave Dynamics. Springer, 268 pp.

  • Petruncio, E. T., , L. K. Rosenfeld, , and J. D. Paduan, 1998: Observations of the internal tide in Monterey Canyon. J. Phys. Oceanogr., 28, 18731903.

    • Search Google Scholar
    • Export Citation
  • Petruncio, E. T., , J. D. Paduan, , and L. K. Rosenfeld, 2002: Numerical simulations of the internal tide in a submarine canyon. Ocean Modell., 4 (3–4), 221248, doi:10.1016/S1463-5003(02)00002-1.

    • Search Google Scholar
    • Export Citation
  • Rainville, L., , T. M. S. Johnston, , G. S. Carter, , M. A. Merrifield, , R. Pinkel, , P. F. Worcester, , and B. D. Dushaw, 2010: Interference pattern and propagation of the M2 internal tide south of the Hawaiian Ridge. J. Phys. Oceanogr., 40, 311325.

    • Search Google Scholar
    • Export Citation
  • Ramp, S. R., , J. D. Paduan, , I. Shulman, , J. Kindle, , F. L. Bahr, , and F. Chavez, 2005: Observations of upwelling and relaxation events in the northern Monterey Bay during August 2000. J. Geophys. Res.,110, C07013, doi:10.1029/2004JC002538.

  • Rosenfeld, L. K., , F. B. Schwing, , N. Garfield, , and D. E. Tracy, 1994: Bifurcated flow from an upwelling center: a cold water source for Monterey Bay. Cont. Shelf Res., 14, 931964, doi:10.1016/0278-4343(94)90058-2.

    • Search Google Scholar
    • Export Citation
  • Shea, R. E., , and W. W. Broenkow, 1982: The role of internal tides in nutrient enrichment of Monterey Bay, California. Estuarine Coastal Shelf Sci., 15, 5766.

    • Search Google Scholar
    • Export Citation
  • Slinn, D., , and M. Levine, 2003: Modeling internal tides and mixing over ocean ridges. Dynamics of Oceanic Internal Gravity Waves, II: Proc. ‘Aha Huliko‘a Hawaiian Winter Workshop, Honolulu, HI, University of Hawaii at Manoa, 59–68.

  • Swart, N. C., , S. E. Allen, , and B. J. W. Greenan, 2011: Resonant amplification of subinertial tides in a submarine canyon. J. Geophys. Res.,116, C09001, doi:10.1029/2011JC006990.

  • Thorpe, S., 1977: Turbulence and mixing in a Scottish loch. Philos. Trans. Roy. Soc. London, 286A, 125181.

  • Wunsch, C., , and S. Webb, 1979: The climatology of deep ocean internal waves. J. Phys. Oceanogr., 9, 235243.

  • Xu, J. P., , and M. A. Noble, 2009: Currents in Monterey Submarine Canyon. J. Geophys. Res.,114, C03004, doi:10.1029/2008JC004992.

  • Zhao, Z., , M. H. Alford, , J. A. MacKinnon, , and R. Pinkel, 2010: Long-range propagation of the semidiurnal internal tides from the Hawaiian Ridge. J. Phys. Oceanogr., 40, 713736.

    • Search Google Scholar
    • Export Citation
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    (a) Map of the upper MSC. The red line denotes the canyon’s thalweg, or deepest path. The along-thalweg distance is marked with black dots at 1-km intervals and labeled at 5-km intervals. Isobaths are shown at 50-m intervals, with contours at 200-m intervals bold and labeled at left. The Wain et al. (2012, manuscript submitted to J. Geophys. Res.) SWIMS3 tracks are shown in light yellow. At each mooring, the depth-integrated semidiurnal energy and flux are shown with circles and arrows, respectively. Green and blue colors indicate time averages over the first spring-neap cycle (yearday 48–62) and the successive three (yearday 62–106), respectively. (b) Map of Monterey Bay and adjacent region. The green box shows the upper MSC as shown in (a).

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    A 5-day segment of the MP2 measurements. (a) Eastward velocity. (b) Northward velocity. In (a),(b), the velocity data between 6- and 40-m depths are from a 300-kHz ADCP. (c) Temperature. Data between 18- and 40-m depths are from a string of HOBO thermistors. Isothermal contours are shown every 0.5°C and labeled every 1°C. (d) Salinity. The gray lines in (d) represent the MP’s depth along the mooring cable, making a round trip from 40-m depth to 10-m height above the bottom each 80 min.

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    A 5-day segment of the LR4 measurements: (a) eastward velocity, (b) northward velocity, (c) upward velocity, and (d) temperature at nine depths. Isothermal contours are shown every 0.5°C and labeled every 1°C. Linear interpolation is used to obtain the contours.

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    Frequency spectra of (a),(b) rotary velocity and (c),(d) displacement at MP2 and LR4, respectively. Outstanding tidal peaks are labeled.

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    Frequency spectra of MP2 measurements at 200-m depth, superimposed with GM76. The vertical gray band indicates the semidiurnal bandpass filter used in this study.

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    (a)–(c) Barotropic tidal height. (a) Measurements from MP2’s SBE #6622 (gray) and Monterey tide gauge station (black). (b) The semidiurnal constituent (M2 + S2 + N2 + K2) and (c) the diurnal constituent (O1 + K1 + P1 + Q1). (d)–(f) Depth-averaged currents at MP2 (u// denotes along local isobath, i.e., toward 60° true). (d) Meaured, (e) semidiurnally bandpassed, and (f) harmonic constituent (M2 + S2 + N2 + K2).

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    Background wind, stratification and currents. (a) Wind vectors at NOAA buoy #46042 (see Fig. 1b for location), showing upwelling-favorable northwestly wind beginning yearday 65, except for a 5-day relaxation during yearday 95–100. (b) Temperature, (c) salinity, and (d) stratification measured at MP2 and smoothed by a 2.1-day sliding window. In (b),(c),(d), the black lines indicate the pycnocline depth before the storm; while during the storm the pycnocline depth rose to near surface and cannot be accurately determined. (e) Eastward and (f) northward velocity low-pass filtered by a fourth-order Butterworth filter with a 5-day cutoff period.

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    Comparison of buoyancy frequency profiles from moorings (colors) and a CTD station 100 km to the west (see Fig. 1b for location). The CTD station was in 3700 m water; only the upper 0–500 m is plotted.

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    Comparison of semidiurnal (a) HKE, (b) APE, and (c) flux magnitude at MP2, estimated using the time-averaged and -varying stratifications, respectively. Each quantity is computed as the sum over the lowest ten modes.

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    Time-varying buoyancy frequency and baroclinic modes. (a) MP2 observed buoyancy frequency profiles on yearday 55 and 92. (b),(c) Baroclinic modes (yearday 55 solid; 92 dashed) derived from the buoyancy frequency profiles shown in (a): (b) velocity modes and (c) displacement modes. The first three baroclinic modes are in red, blue, and green, respectively. (d) Zero-crossing depth [e.g., indicated by brown dots in (b)] of the first baroclinic mode for velocity. (e) Eigenvalue, phase speed, and group speed of the first baroclinic mode.

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    Semidiurnal internal tides at MP2. (a) Eastward velocity, (b) northward velocity, (c) vertical displacement, (d) horizontal kinetic energy (hke), (e) available potential energy (ape), (f) eastward energy flux, (g) northward energy flux, (h) HKE, (i) APE, (j) E, and (k) flux magnitude. In (h)–(k), the lowest 10 baroclinic modes are extracted, and modes 1–5 are shown as stacked histograms.

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    Semidiurnal internal tides at LR4. (a) Eastward velocity, (b) northward velocity, and (c) vertical displacement. (d)–(g) Depth-integrated quantities computed as the sum over the first three modes: (d) HKE, (e) APE, (f) E, and (g) flux magnitude.

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    Time-mean modal distribution of semidiurnal HKE, APE, and F at MP2.

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    Time series of (a)–(d) the moored semidiurnal energy and flux and (e),(f) barotropic forcing: (a) HKE at LR1–LR3 and WH1; (b) HKE at MP1–MP3 and LR4: (c) APE; (d) flux magnitude; (e) semidiurnal barotropic tidal height; and (f) depth-averaged current at MP2 (toward 60° true). In (e),(f), the times of the four spring tides SP1–SP4 are highlighted in gray. In (a)–(d), the vertical lines give the maximum value of each quantity at each spring tide. Note the scale difference between (a),(b) HKE and (c) APE.

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    Mode-1 standing and progessive waves. (a) The HKE to APE ratio rE. The horizontal black line indicates the theoretical value of ~2.2. (b) The ratio of flux magnitude to total energy, , estimated from the moorings (colored lines). The theoretical group speed cg (black line for MP1; gray band for MP2, MP3, and LR4) is a function of time owing to the varying stratification. The vertical spread of the gray band accounts for the varying water depth at the moorings, on which cg also depends. (c) Greenwich phase of mode-1 M2 displacement.

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    Vertical profiles of along-canyon energy flux at MP1–MP3 and LR4 on yearday (a) 56 and (b) 86. The along-canyon bathymetry is plotted, and internal tide characteristics for each stratification profile are overlaid. The width of the gray bands shows the spread of characteristics during yearday (a) 53–59 and (b) 83–89.

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    Turbulent dissipation rate at MP2 and MP3. (a) Semidiurnal and diurnal barotropic tidal forcing. (b) Semidiurnal energy flux. (c) Depth-integrated dissipation rate at MP2 and MP3, smoothed with a 4-day running window. (d) Turbulent dissipation rate measured at MP2, and smoothed using a 1-day running window. (e) As in (d), but for MP3. In (d),(e) the y axis is height above the bottom (HAB) in meters.

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    Bathymetry in the vicinity of MP2 and semidiurnal tidal excursions averaged over the bottom 100 m for each spring tide period. See the gray box in Fig. 1a for location.

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    Velocity, displacement, and dissipation rate during the (left) first and (right) last spring tides at MP2. (a),(b) Velocity u//, that is, toward 60° true; (c),(d) turbulent dissipation rate; and (e),(f) semidiurnal velocity (blue), displacement (red), and dissipation rate (green) averaged over the bottom 100 m.

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    Energy and flux errors due to data gaps at MP2 and MP3. (a)–(d) Vertical profiles of u, η variance at (a),(b) MP2 and (c),(d) MP3. Gaps are shown in red. (e) APE, (g) HKE, and (i) flux magnitude at MP2 obtained from both the raw and filled data. (f),(h),(j) As in (e),(g),(i) but for MP3.

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    Comparison of depth-averaged HKE computed from modal fits (colors) and direct integration (black) at the ADCP moorings.

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Internal Tides and Mixing in a Submarine Canyon with Time-Varying Stratification

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  • 1 Applied Physics Laboratory, University of Washington, Seattle, Washington
  • | 2 Applied Physics Laboratory and School of Oceanography, University of Washington, Seattle, Washington
  • | 3 Department of Oceanography, University of Hawaii at Manoa, Honolulu, Hawaii
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Abstract

The time variability of the energetics and turbulent dissipation of internal tides in the upper Monterey Submarine Canyon (MSC) is examined with three moored profilers and five ADCP moorings spanning February–April 2009. Highly resolved time series of velocity, energy, and energy flux are all dominated by the semidiurnal internal tide and show pronounced spring-neap cycles. However, the onset of springtime upwelling winds significantly alters the stratification during the record, causing the thermocline depth to shoal from about 100 to 40 m. The time-variable stratification must be accounted for because it significantly affects the energy, energy flux, the vertical modal structures, and the energy distribution among the modes. The internal tide changes from a partly horizontally standing wave to a more freely propagating wave when the thermocline shoals, suggesting more reflection from up canyon early in the observational record. Turbulence, computed from Thorpe scales, is greatest in the bottom 50–150 m and shows a spring-neap cycle. Depth-integrated dissipation is 3 times greater toward the end of the record, reaching 60 mW m−2 during the last spring tide. Dissipation near a submarine ridge is strongly tidally modulated, reaching 10−5 W kg−1 (10–15-m overturns) during spring tide and appears to be due to breaking lee waves. However, the phasing of the breaking is also affected by the changing stratification, occurring when isopycnals are deflected downward early in the record and upward toward the end.

Corresponding author address: Zhongxiang Zhao, Applied Physics Laboratory, University of Washington, 1013 NE 40th Street, Seattle, WA 98105. E-mail: zzhao@apl.washington.edu

Abstract

The time variability of the energetics and turbulent dissipation of internal tides in the upper Monterey Submarine Canyon (MSC) is examined with three moored profilers and five ADCP moorings spanning February–April 2009. Highly resolved time series of velocity, energy, and energy flux are all dominated by the semidiurnal internal tide and show pronounced spring-neap cycles. However, the onset of springtime upwelling winds significantly alters the stratification during the record, causing the thermocline depth to shoal from about 100 to 40 m. The time-variable stratification must be accounted for because it significantly affects the energy, energy flux, the vertical modal structures, and the energy distribution among the modes. The internal tide changes from a partly horizontally standing wave to a more freely propagating wave when the thermocline shoals, suggesting more reflection from up canyon early in the observational record. Turbulence, computed from Thorpe scales, is greatest in the bottom 50–150 m and shows a spring-neap cycle. Depth-integrated dissipation is 3 times greater toward the end of the record, reaching 60 mW m−2 during the last spring tide. Dissipation near a submarine ridge is strongly tidally modulated, reaching 10−5 W kg−1 (10–15-m overturns) during spring tide and appears to be due to breaking lee waves. However, the phasing of the breaking is also affected by the changing stratification, occurring when isopycnals are deflected downward early in the record and upward toward the end.

Corresponding author address: Zhongxiang Zhao, Applied Physics Laboratory, University of Washington, 1013 NE 40th Street, Seattle, WA 98105. E-mail: zzhao@apl.washington.edu

1. Introduction

Submarine canyons of various shapes and sizes are common features on continental shelves and slopes, occupying as much as 40% of continental slopes on the west coast of the United States by some measures (Hickey 1995). Because of their ability to focus internal waves (Gordon and Marshall 1976; Wunsch and Webb 1979; Hotchkiss and Wunsch 1982), they have long been identified as potential sites of intense internal wave activity and elevated turbulent mixing, and thus are likely important in processes such as the large-scale circulation as well as primary productivity and particle transport along the coast (e.g., Shea and Broenkow 1982; Hunkins 1988; Gardner 1989; Paull et al. 2005; Lee et al. 2009). Observations in submarine canyons indeed find diapycnal diffusivities Kρ up to 10−2 m2 s−1, three orders of magnitude greater than the open ocean value of O(10−5 m2 s−1) (e.g., Lueck and Osborn 1985; Carter and Gregg 2002; Carter et al. 2005; Gregg et al. 2005). However, parameterizations of the mixing in terms of the usual internal wave cascades underpredict the measured levels by two orders of magnitude (Kunze et al. 2002), indicating different and/or additional mixing processes are likely at play in canyons than in the ocean interior.

The energy source for the turbulence is assumed to be the internal tides propagating in through their mouth or ocean end (though the possible additional role of baroclinic conversion within them has not been ruled out; Wain et al. 2012, manuscript submitted to J. Geophys. Res.). Therefore, understanding the manner in which remotely incident internal tides propagate inside canyons, navigate around their bends, and reflect off their steep walls is key to determining the total dissipation within canyons and its horizontal and depth distribution, both of which are necessary for determining the buoyancy flux.

Monterey Submarine Canyon (MSC), the largest submarine canyon on the US west coast, has been the site of a number of observational and modeling studies in recent years (e.g., Petruncio et al. 1998; Kunze et al. 2002; Carter and Gregg 2002; Jachec et al. 2006; Hall and Carter 2011). MSC runs across the continental shelf of Monterey Bay, with its head just off Moss Landing, California (Fig. 1). It features a winding thalweg (red), in contrast to some other canyons that are relatively straight (e.g., Ascension and Kaoping, Gregg et al. 2011; Lee et al. 2009). Starting at the canyon mouth, there are three sharp bends along the canyon thalweg (Carter 2010): the San Gregorio, Monterey, and Gooseneck meanders (Fig. 1b), the latter of which (Fig. 1a) is studied here in detail with a set of 8 moorings. Simultaneous shipboard surveys are reported separately by Wain et al. (2012, manuscript submitted to J. Geophys. Res.).

Fig. 1.
Fig. 1.

(a) Map of the upper MSC. The red line denotes the canyon’s thalweg, or deepest path. The along-thalweg distance is marked with black dots at 1-km intervals and labeled at 5-km intervals. Isobaths are shown at 50-m intervals, with contours at 200-m intervals bold and labeled at left. The Wain et al. (2012, manuscript submitted to J. Geophys. Res.) SWIMS3 tracks are shown in light yellow. At each mooring, the depth-integrated semidiurnal energy and flux are shown with circles and arrows, respectively. Green and blue colors indicate time averages over the first spring-neap cycle (yearday 48–62) and the successive three (yearday 62–106), respectively. (b) Map of Monterey Bay and adjacent region. The green box shows the upper MSC as shown in (a).

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

Model simulations and field observations confirm a substantial incident semidiurnal baroclinic energy flux at the canyon mouth; specifically, that the Sur Plateau (Fig. 1b) is the primary source of internal tides into MSC (e.g., Jachec et al. 2006; Hall and Carter 2011; Johnston et al. 2011; Kang and Fringer 2012). At the mouth of the canyon, the modeled cross-section up-canyon energy flux is about 9 MW (Hall and Carter 2011; Kang and Fringer 2012), agreeing well with measurements by Kunze et al. (2002). In the lower MSC, the canyon is usually subcritical (i.e., less steep than semidiurnal internal-wave characteristics) in the along-thalweg direction so that semidiurnal internal tides are topographically steered around the gentler Monterey and San Gregorio meanders (Petruncio et al. 2002; Jachec et al. 2006; Hall and Carter 2011). However, the internal tide does not appear to follow the sharper bend at Gooseneck Meander (Hall and Carter 2011; Wain et al. 2012, manuscript submitted to J. Geophys. Res.). As a result, the baroclinic velocities lead to flow perpendicular to the ridge near the bend, leading to a breaking lee wave that dominates the dissipation in the upper canyon (Wain et al. 2012, manuscript submitted to J. Geophys. Res.).

Recently, the role of low-frequency flows and stratification changes has become recognized in modulating the generation and propagation of internal tides in the open ocean (Alford and Zhao 2007a; Kelly et al. 2012), their reflection from continental margins (Klymak et al. 2011), their propagation on continental shelves (MacKinnon and Gregg 2003a,b; Kurapov et al. 2003), and the interference patterns that arise from multiple waves (Alford et al. 2006). In MSC, Petruncio et al. (1998) observed progressive and standing waves in field experiments conducted in April and October 1994, respectively, and they attributed the difference to changes in stratification between the two experiments. In the work presented here, we demonstrate that the shoaling of the thermocline associated with springtime upwelling-favorable winds markedly affects the patterns of velocity, displacement, energy, and energy flux, supporting model predictions by Hall and Davies (2007), Kurapov et al. (2010), and Osborne et al. (2011), and observations by Petruncio et al. (1998). In our case, the stratification changes are substantial enough to necessitate their incorporation into the energy flux and modal structure calculations; use of a time-mean stratification results in substantial errors. The deeper thermocline during the first period results in greater energy but similar net up-canyon energy flux, implying greater flux from further up canyon. Though we cannot determine whether greater reflection of the incident waves, or stronger up-canyon conversion, is responsible, ray analysis indicates the along-canyon slope changes from supercritical to near-critical, suggesting the former. Additionally, turbulent dissipation, which we estimate via Thorpe scales (Thorpe 1977; Dillon 1982) appears to be phased differently relative to the baroclinic flows in the two periods, with depth-integrated values nearly a factor of 2 greater later in the record.

2. Data, techniques, and oceanographic background

a. Experiment

The field experiment was conducted via two cruises onboard R/V Wecoma in February and April 2009, respectively. During the first cruise, eight moorings were deployed on 17–18 February (yearday 47–48; Fig. 1a). We refer to time using yearday, which is defined as the decimal days starting from midnight on 31 December 2008 UTC. Of the eight moorings, three consisted primarily of a McLane moored profiler (MP) and were labeled as MP1, MP2, and MP3, respectively. Four moorings were instrumented with bottom mounted 75-kHz long-range acoustic Doppler current profilers (ADCPs) and were labeled as LR1, LR2, LR3, and LR4. LR4 was hooked around yearday 92.93, likely by a midwater trawler, and dragged several hundred meters before being freed. Fortunately, none of the instruments was damaged. The eighth mooring contained a 300-kHz Workhorse ADCP, labeled WH1. In the second cruise, WH1 was first recovered on 13 April 2009, and redeployed in the Ascension Canyon experiment (Gregg et al. 2011), and the other seven moorings were recovered on 16–17 April. Detailed instrument configurations of the moorings are listed in Table 1.

Table 1.

Mooring information and instrument configurations. An ADCP contains internal temperature and pressure sensors. Variable U indicates the three-dimensional measurement and u indicates the horizontal two-dimensional measurement.

Table 1.

The moorings ranged from ~19 km (LR1) to ~2 km (WH1) from the canyon head, with the water depth ranging from 604 m at LR1 to 153 m at WH1 (Fig. 1a). The ADCP moorings (LR1–LR4 and WH1) were deployed along the canyon’s thalweg (Fig. 1a, red), whereas the MP moorings (MP1–MP3) were on the canyon’s southern flank.

The along- and cross-canyon structure of the energy flux and dissipation rate were investigated on the second cruise using SWIMS3, a towed profiler (Gregg et al. 2011; Wain et al. 2012, manuscript submitted to J. Geophys. Res.), along 16 cross-canyon sections (Fig. 1a, light yellow lines). We focus here on mooring observations, referring interested readers to Wain et al. (2012, manuscript submitted to J. Geophys. Res.) for the spatial features revealed with the SWIMS3 surveys.

b. MP moorings

On each MP mooring (MP1–MP3), a McLane Moored Profiler (MP) crawled up and down along the cable between about 40-m depth and 10 m above the bottom. Each MP moved along the cable at a speed of 0.25 m s−1, carrying a Falmouth Scientific acoustic current meter and a conductivity–temperature–depth instrument (CTD) to measure profiles of horizontal velocity, temperature, and salinity. The vertical resolution of gridded velocity and density are about 10 and 2 m, respectively (Doherty et al. 1999; Alford 2010). For MP1–MP3, the water depths were 600, 377, and 288 m, respectively; thus single profiles occurred each 60, 40, and 30 min. Velocity measurements above each MP were made using an upward looking 300-kHz ADCP (Table 1). Subsurface pressure measurements at each mooring revealed that mooring pulldown was only 1–2 m owing to very taut design.

MP2 and MP3 performed well for their two-month mission, each covering a total vertical distance of about 650 km (2068 and 2760 profiles, respectively). Unfortunately, MP1 stopped profiling after only 11 days due to a mechanical problem.

At MP2, temperature above the MP profiling range was measured with a chain of 10 HOBO thermistors covering 18–36 m (Table 1). The instruments were attached to the top of the mooring’s main subsurface float, with a weak link to avoid endangering the main mooring in case the top HOBO chain, which was nominally at only 10 m depth, was hooked by fishing activity. The HOBO thermistors sampled every 40 min, matching MP2’s temporal resolution. The nominal resolution and accuracy of the HOBO thermistors is 0.10°C, substantially poorer than that of Sea-Bird instruments (0.001°C). Nonetheless, the resolution was more than sufficient to resolve the large temperature signals in the upper 40 m at our site, and the poor accuracy was addressed by cross-calibration with the SBE39 (#3134, Table 1) tethered with the uppermost HOBO thermistor. RMS differences between the SBE39 and the HOBO were well below 0.10°C after calibration.

A 5-day sample of the merged measurements at MP2 is shown in Fig. 2. The velocity measurements from the MP and ADCP, and the temperature measurements from the MP and HOBOs, visually agree on either side of a narrow gap near 40 m (white). Aside from additional small gaps near the top and bottom, the depth coverage is nearly complete. Coverage in velocity is similar at MP1 and MP3, but those moorings have no temperature above 40 m (see the appendix).

Fig. 2.
Fig. 2.

A 5-day segment of the MP2 measurements. (a) Eastward velocity. (b) Northward velocity. In (a),(b), the velocity data between 6- and 40-m depths are from a 300-kHz ADCP. (c) Temperature. Data between 18- and 40-m depths are from a string of HOBO thermistors. Isothermal contours are shown every 0.5°C and labeled every 1°C. (d) Salinity. The gray lines in (d) represent the MP’s depth along the mooring cable, making a round trip from 40-m depth to 10-m height above the bottom each 80 min.

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

Semidiurnal signals dominate the velocity, temperature, and salinity measurements. Velocities and isopycnal displacements are vigorous (~0.6 m s−1 and 100 m peak to peak, respectively), and visibly dominated by the first two vertical modes. A striking feature is the visual shoaling of the thermocline over the course of the five days, associated with the reestablishment of upwelling winds after a storm. The zero crossing of the observed baroclinic velocities responds in kind, moving upward from about 300 m to less than 200 m over the 5-day period. The strong variability of the stratification and the associated structure of the internal motions on such short time scales clearly indicates a need to properly account for time-variable stratification, which is the focus of the present study.

c. ADCP moorings

Each ADCP mooring (LR1–LR4) had an upward-looking 75-kHz ADCP (300-kHz for WH1) 10 m above the bottom. Their bin sizes were 4, 8, or 16 m (see Table 1). All ADCPs sampled at 30-s intervals, and were averaged into 5-min ensembles to reduce measurement noise. In addition to the 10-m gap beneath the instrument, the upper 20–40 m (10%–15% of the water depth) are discarded because of contamination by the reflection of side-lobes from the surface.

Because of the lack of density or temperature measurements, the ADCP moorings cannot detect vertical displacements. The exception was LR4, which included a chain of nine Sea-Bird 39 temperature loggers, spanning 33- to 280-m depth (10 m above the bottom) with a 33-m spacing (Table 1). Thus, low-mode energy flux and available potential energy can be estimated at LR4, but only kinetic energy can be measured at the other ADCP moorings.

Figure 3 shows sample measurements at LR4 during the same period as Fig. 2 for MP2. Again, the dominance of the semidiurnal tidal signals and the upward migration of the zero crossings in velocity are apparent. The temperature measurements, though only at 9 depths, successfully captured both the low-frequency variation and the semidiurnal motions (Fig. 3d). The spikes in vertical velocity measurements (Fig. 3c), which appear to be internal tidal bores and/or nonlinear waves, similar to those reported by Key (1999) and Carter et al. (2005), will be reported elsewhere.

Fig. 3.
Fig. 3.

A 5-day segment of the LR4 measurements: (a) eastward velocity, (b) northward velocity, (c) upward velocity, and (d) temperature at nine depths. Isothermal contours are shown every 0.5°C and labeled every 1°C. Linear interpolation is used to obtain the contours.

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

d. Vertical displacement

The MP moorings measured temperature and salinity, but LR4 measured only temperature. Because temperature dominates over salinity in determining density in MSC, vertical displacement is calculated from temperature measurements at each mooring, where T(z, t) is the temperature measurement, is the time averaged temperature and Tz(z, t) is the temperature gradient determined from MP2. and Tz(z, t) are smoothed using a 2.1-day sliding window (four semidiurnal periods) to account for slow (nontidal) variations in the background stratification. Tz(z, t) at MP2 is used for the calculation at all moorings because of its full-depth coverage because lateral differences are small.

To ensure that salinity signals do not influence displacement computed from temperature, the displacement was also computed using potential density at the MP moorings. The RMS differences between isotherm and isopycnal displacements are less than 1 m (compared to the measured displacements of tens of meters; Fig. 2), indicating the dominance of temperature in setting density in the canyon.

e. Frequency spectra

The sample data (Figs. 2 and 3) make the dominance of the semidiurnal tide obvious; this statement is quantified by examining frequency spectra of velocity and displacement as functions of depth (Fig. 4). Because spectra from all locations are similar, only those from MP2 and LR4 are plotted. For velocity, the rotary spectrum (Mooers 1970; Gonella 1972) is computed, with negative and positive frequencies indicating counterclockwise (CCW) and clockwise (CW) rotation in time, respectively.

Fig. 4.
Fig. 4.

Frequency spectra of (a),(b) rotary velocity and (c),(d) displacement at MP2 and LR4, respectively. Outstanding tidal peaks are labeled.

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

For both the velocity and displacement spectra, the semidiurnal tidal constituents are dominant. They appear as wide bands (as opposed to lines), likely due to the presence of incoherent constituents. The presence of overtides and compound tides (e.g., MK3, M4, M6) indicate a degree of nonlinearity to the internal tide field. Similar spectral features have been observed previously in MSC (Key 1999; Kunze et al. 2002; Carter et al. 2005).

All tidal constituents are bottom intensified, consistent with previous field observations (Carter and Gregg 2002; Xu and Noble 2009). In contrast, near-inertial motions are surface intensified due to their generation at the surface by the wind (e.g., Paduan and Rosenfeld 1996). In our data, they appear as a wide patch around f in the CW component of the velocity spectra (Figs. 4a,b), but not in the displacement spectra (Figs. 4c,d). Near-inertial motions extend to about 200 m and 80 m depth at MP2 and LR4, respectively.

MSC lies poleward of the turning latitude of the diurnal internal tide, that is, ωo1, K1 are lower than the local inertial frequency f ≡ 2Ω sin(latitude), where Ω is the rotation rate of the earth. Therefore, progressive diurnal internal tides are not allowed; nonetheless trapped diurnal internal tides may exist (e.g., Dale et al. 2001; Swart et al. 2011). The displacement spectra show diurnal peaks of similar magnitude to the semidiurnal constituent (Figs. 4c,d), indicating the motions are indeed baroclinic and not simply the diurnal barotropic tides. They appear to be vertical displacements caused by trapped diurnal internal tides, and will be reported elsewhere.

Figure 5 presents the velocity and displacement spectra from MP2 measurements at 200-m depth, with the Garrett-Munk (GM76) spectrum superimposed for comparison (Garrett and Munk 1975; Cairns and Williams 1976). The measured spectral level is higher than GM76 throughout most of the frequency range. The spectra levels from measurements closer to bottom (such as at 300-m depth) are even higher. This is consistent with previous observations that internal waves are elevated in canyons (Hotchkiss and Wunsch 1982; Carter and Gregg 2002).

Fig. 5.
Fig. 5.

Frequency spectra of MP2 measurements at 200-m depth, superimposed with GM76. The vertical gray band indicates the semidiurnal bandpass filter used in this study.

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

f. Barotropic tide

As measures of the barotropic tide, we compute sea level and depth-averaged currents at our moorings, though measurements near the modeled generation site at Sur Plateau would obviously be preferable. For sea level, 18 sets of moored pressure measurements (Table 1) are examined. When the mean deployment depth is subtracted, they agree very well with each other and with measurements at the Monterey tide station at 36°36.3′N, 121°53.2′W (Fig. 1b, red square). A sample comparison at MP2 is shown in Fig. 6a. The close agreement indicates both minimal mooring pulldowns, as asserted earlier, and a very small degree of spatial variability in tidal sea level across the bay, as reported in a numerical model by Carter (2010).

Fig. 6.
Fig. 6.

(a)–(c) Barotropic tidal height. (a) Measurements from MP2’s SBE #6622 (gray) and Monterey tide gauge station (black). (b) The semidiurnal constituent (M2 + S2 + N2 + K2) and (c) the diurnal constituent (O1 + K1 + P1 + Q1). (d)–(f) Depth-averaged currents at MP2 (u// denotes along local isobath, i.e., toward 60° true). (d) Meaured, (e) semidiurnally bandpassed, and (f) harmonic constituent (M2 + S2 + N2 + K2).

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

Harmonic constants are extracted by harmonic analysis using the T_TIDE toolbox (Pawlowicz et al. 2002). For all moorings, the harmonic tidal constituents account for more than 95% of the pressure variance. Compared with Monterey tide station, the overall RMS differences are 1.3 cm and 3.8° for the M2 amplitude and phase, respectively. The semidiurnal and diurnal tidal variations are shown in Figs. 6b,c, respectively.

Barotropic current is estimated as the depth average of the moored velocity measurements at MP2, where the near-complete depth coverage minimizes risk of aliasing baroclinic motions onto the estimate of barotropic current (a real concern as the depth average is about 0.15 m s−1 at most compared to 0.6 m s−1 for the baroclinic motions). Total barotropic velocity (u// denotes the velocity component along local isobath; Fig. 6d) is substantially more variable than the corresponding quantity for sea level, which is completely dominated by the astronomical forcing and shows little variation across the bay. When the semidiurnal components are isolated using T_TIDE and bandpass filtering (Figs. 6e,f), a spring-neap cycle is seen, but with timing of the springs (SP1–SP4) that differs somewhat from that of sea level (Fig. 6b, SP1–SP4). Specifically, the second and fourth spring tides occur several days later in currents than sea level. This is surprising given the general impression of the barotropic tide as generally more deterministic. However, phase differences between tidal height and barotropic velocity do exist owing to a feedback between internal tides in the canyon and the barotropic velocities (Carter 2010). Though the details remain to be explored, the feedback appears to arise because internal tides alter the distribution of total pressure, which affects the structure of the barotropic tide velocities, that in turn generate the internal tides.

g. Low-frequency variations in stratification and current

Low-pass filtered temperature and salinity at MP2 over the course of the 2-month mooring deployments, plotted in Figs. 7b,c, are compared with wind measured at National Oceanic and Atmospheric Administration (NOAA) buoy 46042 (36°47.12′N, 122°28.15′W), about 50 km to the west (Fig. 1b, red triangle). Our observations do not resolve the full complexity of the ocean response, which is likely three-dimensional (Rosenfeld et al. 1994) and larger-scale than our study. However, the observed winds and ocean response are consistent with the typical situation in early spring on the California coast observed in detailed larger-scale studies (e.g., Rosenfeld et al. 1994; Ramp et al. 2005). Early in the record, relatively warm, freshwater is present in the upper 100 m. As stormier winter weather transitions to more persistent upwelling-favorable winds near yearday 65 (Fig. 7a), it disappears. For a 5 m s−1 wind, the rising velocity of bottom water may reach several cm per hour, so that the ocean has a short response time (Ramp et al. 2005). Later in the record, when the upwelling winds lapse for a few days, a weaker warm, fresh layer reappears before disappearing again by the end of the record. Correspondingly, the thermocline deepens and then shallows again (Figs. 2 and 3).

Fig. 7.
Fig. 7.

Background wind, stratification and currents. (a) Wind vectors at NOAA buoy #46042 (see Fig. 1b for location), showing upwelling-favorable northwestly wind beginning yearday 65, except for a 5-day relaxation during yearday 95–100. (b) Temperature, (c) salinity, and (d) stratification measured at MP2 and smoothed by a 2.1-day sliding window. In (b),(c),(d), the black lines indicate the pycnocline depth before the storm; while during the storm the pycnocline depth rose to near surface and cannot be accurately determined. (e) Eastward and (f) northward velocity low-pass filtered by a fourth-order Butterworth filter with a 5-day cutoff period.

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

Buoyancy frequency is defined as
e1
where g is gravitational acceleration, ρ0 is a reference ocean water density, and is potential density σθ(z, t) smoothed by a 2.1-day sliding window. is slowly varying, and shows a maximum near 100 m beneath the warm, salty water originally present, shoaling as the layer disappears (Fig. 7d). It will be shown below that these changes are associated with substantial alterations in the modal shapes and energy fluxes.

As a result of the upwelling-favorable winds, stratification varies not only temporally but also spatially. Water properties at MP1 and MP3 (not shown) track those at MP2, as seen in buoyancy frequency profiles at the beginning of the first cruise (yearday 49, Fig. 8). All three MP’s (colors) agree closely, but a time-mean CTD profile 100 km to the west (36°36.5′N, 123°00′W; Fig. 1b, red cross) differs sharply. The CTD profile was computed from the mean of 7 profiles taken over the same 12-h period as that of the MP profiles, to average out tidal heaving. The CTD profile at the same deep-water location taken during the second cruise in April differed little from that in February, supporting that offshore stratification is much less variable.

Fig. 8.
Fig. 8.

Comparison of buoyancy frequency profiles from moorings (colors) and a CTD station 100 km to the west (see Fig. 1b for location). The CTD station was in 3700 m water; only the upper 0–500 m is plotted.

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

h. Calculating energy and flux in time-variable stratification

Energy and flux are often computed using time-mean stratification profiles. In the open ocean, this is generally a good assumption. Here, as in many coastal locations, stratification varies enough that it must be taken into account in computing energy and energy flux. Additionally, stratification alters the mode shapes, affecting the modal distribution of all three quantities. These effects are described here, which are distinct from the changes in the structure of the propagating versus standing wave pattern discussed later.

Energy and flux are computed in the usual ways following the same procedure as described in Kunze et al. (2002), Nash et al. (2005), and Alford and Zhao (2007a), but with stratification allowed to vary slowly in time. Because our focus is the semidiurnal internal tide, all quantities are first run through a fourth-order Butterworth bandpass filter, with the central frequency at 1.93 cycles per day (cpd) and the cutoff frequencies [1.74, 2.13] cpd (Fig. 5, vertical gray band).

Available potential energy (APE) is then given by
e2
and horizontal kinetic energy (HKE) by
e3
where ρ0 is the water density and u′ is the baroclinic current computed by subtracting the depth mean at each time from the measured velocity. The angle brackets indicate an average over one tidal cycle, and ape(z, t) and hke(z, t) are the nondepth-integrated horizontal kinetic and available potential energies, in units of Joules per cubic meter. The total energy E is calculated by
e4
Energy flux F is computed as up′, where the perturbation pressure is computed in the usual way from displacement,
e5
where the surface baroclinic pressure is computed by requiring the depth integral of p′ to be zero:
e6

Figure 9 shows the effect of the time-varying stratification on the depth integral of each quantity. HKE is not affected, but APE and flux magnitude vary by up to 50% when the time-varying stratification is considered.

Fig. 9.
Fig. 9.

Comparison of semidiurnal (a) HKE, (b) APE, and (c) flux magnitude at MP2, estimated using the time-averaged and -varying stratifications, respectively. Each quantity is computed as the sum over the lowest ten modes.

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

Flat-bottom modes are used to describe the wavenumber distribution of the data at each mooring. While the slopes may invalidate their strict use and lead to terms involving mode-mode interactions (Kelly et al. 2012), the freely-propagating part of the signal will nonetheless be estimated below by comparing E and F for each mode following Alford and Zhao (2007a).

Time-varying stratification also affects the shape of the vertical modes and therefore the partition of energy and flux between them. The normal modes for vertical displacement Φ(z) are determined by solving the Taylor–Goldstein equation with zero background flow:
e7
subject to the boundary conditions Φ(0) = Φ(−H) = 0, where n is the mode number, and cn is the eigenspeed (e.g., Gill 1982; Pedlosky 2003). In spite of the ~0.1 m s−1 low-frequency flows evident in Figs. 7e,f, we restrict our attention to the effects of stratification, deferring effects of sheared background flow for another paper. cn is related to the group velocity, cg, and the phase velocity, cp, via the dispersion relationship (Alford and Zhao 2007b). Φ(z) is related to the corresponding modes for pressure and horizontal velocity Π(z) via (Gill 1982):
e8

Vertical gaps in the measurements place severe limitations on the precision of energy and energy flux estimates; however, internal tides can be approximately represented by a superposition of a number of discrete baroclinic modes (Nash et al. 2005). Our water column coverage is excellent at MP2 and decent at the other moorings, allowing us to fit 10 modes at MP2 and 3 modes at the other moorings (see the appendix).

The effect of variable stratification on the modal shapes is demonstrated in Fig. 10. The buoyancy profiles on yearday 55 and 92 (pre- and postupwelling) are shown in Fig. 10a. The corresponding baroclinic modes for velocity and displacement are shown in Figs. 10b,c. The zero-crossing depth of the mode 1 velocity profile (b, brown dots) ranges between 100–200 m (d). During the deployment period the mode 1 group and phase speeds decrease as the stratification weakens (e).

Fig. 10.
Fig. 10.

Time-varying buoyancy frequency and baroclinic modes. (a) MP2 observed buoyancy frequency profiles on yearday 55 and 92. (b),(c) Baroclinic modes (yearday 55 solid; 92 dashed) derived from the buoyancy frequency profiles shown in (a): (b) velocity modes and (c) displacement modes. The first three baroclinic modes are in red, blue, and green, respectively. (d) Zero-crossing depth [e.g., indicated by brown dots in (b)] of the first baroclinic mode for velocity. (e) Eigenvalue, phase speed, and group speed of the first baroclinic mode.

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

3. Observed energy and flux

The full records of baroclinic velocity, displacement, energy, and flux are plotted for MP2 (Fig. 11) and LR4 (Fig. 12). As noted, energy and flux are computed via the sum of modes at LR4 owing to the discrete-depth sampling, so its depth-dependent quantities are not plotted. Baroclinic velocity and displacement both clearly show four spring-neap cycles. Signals at spring tide are visually greatest near the surface and bottom for velocity (Figs. 11a,b and 12a,b), and in the middle of the water column for displacement (Figs. 11c and 12c), consistent with a primarily first-mode signal. Energy and flux (Figs. 11d–k and 12d–g) reflect these patterns, with HKE and energy flux magnitude showing shallow and deep maxima and APE greatest at middepth. Again, these imply a primarily first-mode signal, as confirmed in stacked histograms of total depth-integrated energy (Figs. 11h–j and 12d–f) and flux magnitude (Figs. 11k and 12g). The spring-neap cycle is evident in these histograms of energy and flux, with modulation of about a factor of 4. Mode 1 signals contain on average 80% of the energy, as seen by the modal spectrum at MP2 (Fig. 13), with the content in the other modes varying somewhat during the time series.

Fig. 11.
Fig. 11.

Semidiurnal internal tides at MP2. (a) Eastward velocity, (b) northward velocity, (c) vertical displacement, (d) horizontal kinetic energy (hke), (e) available potential energy (ape), (f) eastward energy flux, (g) northward energy flux, (h) HKE, (i) APE, (j) E, and (k) flux magnitude. In (h)–(k), the lowest 10 baroclinic modes are extracted, and modes 1–5 are shown as stacked histograms.

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

Fig. 12.
Fig. 12.

Semidiurnal internal tides at LR4. (a) Eastward velocity, (b) northward velocity, and (c) vertical displacement. (d)–(g) Depth-integrated quantities computed as the sum over the first three modes: (d) HKE, (e) APE, (f) E, and (g) flux magnitude.

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

Fig. 13.
Fig. 13.

Time-mean modal distribution of semidiurnal HKE, APE, and F at MP2.

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

The vertical profile of flux during the first spring is markedly different than at the other three, showing down-canyon fluxes at about 120 m and at depth (Figs. 11f,g). The magnitude of the flux is not greatly different from the other spring tide periods owing to the greater up-canyon flux at shallow depths. However, energy and the ratio of potential to kinetic energy are both significantly greater during the first spring, implying interference from signals traveling down canyon. This assertion will be examined in more detail in section 4.

Mean energy flux averaged over the first spring-neap cycle (Fig. 1, green arrows) and the successive three (blue arrows) is up canyon and generally (but not monotonically) decreases from about 1 to ~0.4–0.5 kW m−1 moving toward the canyon head, as also found by Kunze et al. (2002), Hall and Carter (2011), and Wain et al. (2012, manuscript submitted to J. Geophys. Res.). Flux magnitude does not differ greatly between the first and ensuing spring tides, but the direction changes about 25° at MP2 and a full 90° at LR4. Additionally, total energy (circles) is higher at all moorings in the first spring-neap cycle than the last three.

The spring-neap cycles evident at MP2 and LR4 are present at all moorings in HKE (Figs. 14a,b), and in APE (Fig. 14c) and F (Fig. 14d) at MP1–3 and LR4, the moorings for which these quantities can be computed. Energy and flux rise and fall generally in phase at all moorings, although magnitude is different at each site primarily owing to the patterns of generation and dissipation within the canyon (Hall and Carter 2011; Wain et al. 2012, manuscript submitted to J. Geophys. Res.). The modulation between spring and neap is about a factor of 4 for HKE and flux. Except for at LR4, the modulation of APE is less than that for the other quantities.

Fig. 14.
Fig. 14.

Time series of (a)–(d) the moored semidiurnal energy and flux and (e),(f) barotropic forcing: (a) HKE at LR1–LR3 and WH1; (b) HKE at MP1–MP3 and LR4: (c) APE; (d) flux magnitude; (e) semidiurnal barotropic tidal height; and (f) depth-averaged current at MP2 (toward 60° true). In (e),(f), the times of the four spring tides SP1–SP4 are highlighted in gray. In (a)–(d), the vertical lines give the maximum value of each quantity at each spring tide. Note the scale difference between (a),(b) HKE and (c) APE.

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

Both the timing and the magnitude of energy and flux at each spring (SP1–SP4) are variable. At each site the HKE magnitude at spring tide varies by about 20%–30%, with the greater and lower values poorly predicted by either barotropic tidal height (Fig. 14e) or current (Fig. 14f). To examine the timing of each maximum in the baroclinic quantities relative to the barotropic forcing, the time of the spring tide maxima of energy and flux are determined and shown by different vertical lines in Figs 14a–d. Note that the times of maxima at LR1–LR3 and WH1 are less reliable, because of the large uncertainties in the HKE calculation associated with the surface and bottom gaps (see the appendix). For the first and third spring tides, the observed maxima in the baroclinic quantities occur approximately at the same time as the maxima in both sea level and barotropic current. At the second and fourth spring tides, the observed baroclinic maxima lag those in sea level, but are more or less in line with those in barotropic current. Figure 14 shows that the mismatches (SP2, SP4) occur during the greatest rate of temporal change in the background conditions, and that the good match occurs at SP1 while there is no upwelling or at SP3 while the upwelling is steady.

4. Standing and progressive waves

We hypothesize that the differences between the baroclinic response at the various spring tides arise because of stratification changes associated with spring transition winds (Fig. 7). Specifically, we explore the hypothesis of Petruncio et al. (1998) that internal tides within MSC transition between progressive waves and partly, horizontally standing waves. Their evidence included the horizontal and vertical variations of the phase of the baroclinic velocity and displacements (their Figs. 5 and 11). Here we examine 1) the ratio between horizontal kinetic and available potential energy, 2) the ratio between flux magnitude and total energy compared to the group speed, and 3) the along-channel phase following Petruncio et al. (1998). The three methods all indicate a partly-standing wave early in the record when the thermocline was deeper, transitioning to a more progressive wave later in the record as the thermocline shallowed.

a. HKE/APE ratio

For a progressive semidiurnal internal wave at the latitude of Monterey Submarine Canyon, the HKE to APE ratio rE ≡ (ω2 + f2)/(ω2f2) ≈ 2.2, where ω is the tidal frequency, and f is the local inertial frequency. Two mode-1 waves traveling in opposite directions show an interference pattern wherein APE, HKE, and F all vary with spatial location. Because the minima and maxima of HKE and APE are offset from each other, rE can range from zero to infinity depending on the location of the measurements relative to the nodes and antinodes within the interference pattern (Nash et al. 2004; Alford and Zhao 2007b; Martini et al. 2007). For multiple waves traveling in different directions on a compass rose, the interference patterns can be more complicated still (Rainville et al. 2010; Zhao et al. 2010). However, in general, the cycle mean for a standing and partly-standing wave is less than the theoretical value shown by a progressive wave.

Observed rE at MP1–MP3 and LR4 is shown in Fig. 15a. For all moorings, there is an obvious change before and after yearday 70 (vertical dashed line). Before yearday 70, rE at MP2 (Fig. 15a, blue) is much lower than the theoretical value (black), while after yearday 70 it varies around the theoretical value, suggesting that the internal tide field changed from a partly-standing wave to a progressive wave around yearday 70. MP3 (red) and LR4 (green) display a similar trend, but never reach the theoretical value during the later period, potentially implying spatial variations (examined below).

Fig. 15.
Fig. 15.

Mode-1 standing and progessive waves. (a) The HKE to APE ratio rE. The horizontal black line indicates the theoretical value of ~2.2. (b) The ratio of flux magnitude to total energy, , estimated from the moorings (colored lines). The theoretical group speed cg (black line for MP1; gray band for MP2, MP3, and LR4) is a function of time owing to the varying stratification. The vertical spread of the gray band accounts for the varying water depth at the moorings, on which cg also depends. (c) Greenwich phase of mode-1 M2 displacement.

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

b. Group speed

The ratio of flux magnitude to total energy can also be used to test for progressive versus standing waves. For a progressive wave, equals the group speed cg, with standing or partly-standing waves again showing an interference pattern. In a modally-decomposed wavefield, the degree of free propagation can be assessed for each mode by comparing the observed ratio of flux to energy with the theoretical value of the group speed for each mode (Alford and Zhao 2007b). The technique has been used successfully in a variety of ocean situations (Alford et al. 2006; Alford and Zhao 2007b; Martini et al. 2007; Klymak et al. 2011). Here, is estimated for mode 1 at MP1–MP3 and LR4 (Fig. 15b, colored lines), and compared to the theoretical mode-1 value cg (black line for MP1; gray band for MP2, MP3 and LR4), which also changes in time owing to the changing stratification (Fig. 10). The finite thickness of the mode-1 curve (gray band) represents the dependence on depth, with the upper values corresponding to deeper depths. For all moorings, is less than cg during yearday 48–70, and is close to theoretical values during yearday 70–104, again suggesting partly-standing waves in the first period, and progressive waves in the second period.

c. Greenwich phase

As a final test, we compute the Greenwich phase of mode-1 semidiurnal displacement at each mooring as a function of slowly-varying stratification by harmonic analysis over sliding 2.1-day windows (Fig. 15c). Mode-1 displacement is in phase at all moorings for the first part of the record, a signature of a standing or nearly-standing wave. However, in the second period, phase at MP2, MP3, and LR4 increases shoreward, indicating up-canyon phase propagation. For example, the phase lags between MP2 and MP3 are about 20°–50°, equivalent to 0.7–1.7 h. The propagation times can be compared to that expected from the theoretical phase speed and the distance between the moorings. Taking a phase speed of 0.5–0.7 m s−1 (Fig. 10e) and a 2.5 km MP2–MP3 distance, the propagation time is estimated to be 1–1.4 h. Observed and theoretical free-wave travel times are similar, consistent with a progressive wave.

d. Vertical profiles

The observed pattern of along-canyon energy flux profiles is shown in Fig. 16 for the early period (Fig. 16a) and the late period (Fig. 16b). The flux profiles at MP2, MP3 and LR4 during the later period (Fig. 16b) generally indicate the expected pattern of top- and bottom-intensified up-canyon flux for an up-canyon-propagating mode 1 wave, while during the early period the deep and middepth regions of down-canyon flux are seen that were evident for MP2 in Fig. 11. However, the flux profile at MP1 during this period resembles that expected for a progressive wave, with no reversals. This is consistent with the greater value of at MP1 than at the other locations (Fig. 15b), but not with the values of rE at MP1 or its display of the same phase as the other moorings (Fig. 15c). Hence, the evidence is somewhat conflicting at MP1, but does at least suggest that the partly-standing wave behavior is restricted to up canyon of Gooseneck Meander.

Fig. 16.
Fig. 16.

Vertical profiles of along-canyon energy flux at MP1–MP3 and LR4 on yearday (a) 56 and (b) 86. The along-canyon bathymetry is plotted, and internal tide characteristics for each stratification profile are overlaid. The width of the gray bands shows the spread of characteristics during yearday (a) 53–59 and (b) 83–89.

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

5. Turbulence

Turbulent kinetic energy dissipation rate, ε, is computed from Thorpe scales using the moored potential density data (Thorpe 1977; Dillon 1982; Alford et al. 2006). Given the CTD sample interval of about 0.125 m and its density uncertainty of about 10−4 kg m−3, and the background stratification, overturns of less than a meter can be reliably resolved (Galbraith and Kelley 1996)—much smaller than the observed overturning scales of tens of meters that dominate the dissipation in our data. Dissipation rate is then estimated as
e9
where is the Thorpe scale, and N is the buoyancy frequency.

Dissipation rate for the whole record is plotted in Figs. 17c–e, together with the barotropic tidal forcing (Fig. 17a) and the depth-integrated energy flux (Fig. 17b). Dissipation is bottom-intensified at both locations, with a decay scale of about 50–150 m, as found at these locations and elsewhere in MSC by Carter and Gregg (2002), Kunze et al. (2012), and Wain et al. (2012, manuscript submitted to J. Geophys. Res.). The spring-neap cycle so evident in energy and energy flux (Fig. 17b) appears clearly as a modulation both in this decay scale and in the depth-integrated value (Fig. 17c). However, the modulation is only about a factor of 1.5 or 2, compared to about 4 for the energy flux. The greater dissipation as a fraction of energy flux at neap tides may imply that some of the energy cascades through the internal wave spectrum via nonlinear interactions. Because the time scale for these interactions is a few days, some dissipation at neap tide may result from energy input at the previous spring.

Fig. 17.
Fig. 17.

Turbulent dissipation rate at MP2 and MP3. (a) Semidiurnal and diurnal barotropic tidal forcing. (b) Semidiurnal energy flux. (c) Depth-integrated dissipation rate at MP2 and MP3, smoothed with a 4-day running window. (d) Turbulent dissipation rate measured at MP2, and smoothed using a 1-day running window. (e) As in (d), but for MP3. In (d),(e) the y axis is height above the bottom (HAB) in meters.

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

The intensity of the turbulence and its decay scale are both greater at MP2 than at MP3, likely because MP2 is near the top of a ridge associated with the Gooseneck Meander, and flow is nearly perpendicular to it (Fig. 18 and Wain et al. 2012, manuscript submitted to J. Geophys. Res.). In the vicinity of MP2, depth-integrated dissipation is approximately equal to observed convergent fluxes measured there (Wain et al. 2012, manuscript submitted to J. Geophys. Res.).

Fig. 18.
Fig. 18.

Bathymetry in the vicinity of MP2 and semidiurnal tidal excursions averaged over the bottom 100 m for each spring tide period. See the gray box in Fig. 1a for location.

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

The character of the dissipation is different in the first spring tide period and the subsequent ones, as seen by plotting 2-day time series of along-canyon velocity (Fig. 19, upper panels) and dissipation rate (Fig. 19, middle panels) at MP2.

Fig. 19.
Fig. 19.

Velocity, displacement, and dissipation rate during the (left) first and (right) last spring tides at MP2. (a),(b) Velocity u//, that is, toward 60° true; (c),(d) turbulent dissipation rate; and (e),(f) semidiurnal velocity (blue), displacement (red), and dissipation rate (green) averaged over the bottom 100 m.

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

During the first period (Fig. 19, left panels), dissipation occurs primarily in bursts exceeding 5 × 10−5 W kg−1 once each 12.4 h, when isopycnals at depth are at their deepest (Fig. 19b). The flow in the bottom 100 m at MP2 is oriented perpendicular to a ridge (Fig. 18). Tidal excursion ellipses, computed as the time integral of the semidiurnal velocities averaged over the bottom 100 m, are about ±2 km, causing water to transit the ridge each tidal cycle. Downward deflection of isopycnals occurs following flow to the southwest (Fig. 19a, blue). The geometry and phasing of the dissipation are similar to those collected near a ridge crest in Luzon Strait (Alford et al. 2011), where lee waves formed by baroclinic flow over the ridge become unstable once per period when flow is downslope (Legg and Klymak 2008; Buijsman et al. 2012).

During subsequent spring tide periods (as exemplified by the fourth spring tide, plotted at right in Fig. 19), dissipation is somewhat less deterministic, occurring more continuously throughout the semidiurnal cycle. Some bursts are seen every 12.4 h, but they now occur when isopycnals are at their highest, following flow to the northeast (Fig. 19b). It is possible that the structure of the lee wave response shifts subtly when the stratification changes from a standing (Fig. 19, left) to a progressive-favorable pattern (Fig. 19, right). The overall depth-integrated dissipation increases gradually toward the end of the record (Fig. 17c). It is possible that the greater dissipation contributes to the progressive-wave behavior late in the record by dissipating internal tides that otherwise might have reflected.

6. Discussion

The observed partly standing wave pattern must arise from down-canyon fluxes at MP2, MP3, and LR4 that superpose with the incident up-canyon fluxes. The down-canyon fluxes may arise from greater generation up canyon of the moorings, or greater reflection of the incident fluxes. The tendency of internal waves to back-reflect from topography depends on the relative slope of the wave characteristics relative to the topography. That is, waves with characteristic slopes steeper than the topography will forward reflect, while wave slopes shallower than the topography will back-reflect. Waves with slopes near the topographic slope will undergo “critical reflection” (Eriksen 1982), wherein the vertical wavenumber of the reflected waves becomes large, and energy density enhances, breaks, and dissipates. Numerical simulations of waves incident upon critically-sloping topography show formation of internal tidal bores and elevated mixing (Slinn and Levine 2003).

To compare the wave slopes in the two different periods to the topographic slope, early- and late-period characteristics are computed from the stratification profile at yearday 56 ± 3 and 86 ± 3 by integrating the wave slope,
e10
These characteristics are initialized at an arbitrary along-canyon location (here chosen as 5 km from the canyon head; Fig. 16). The thalweg slope (gray shading) is fairly constant spatially, with a slope of about 0.025. For the early stratification (Fig. 16a), semidiurnal characteristics are shallower than the thalweg, suggesting back reflection consistent with the observed flux profiles indicating flux in both directions. For the later period (Fig. 16b), the altered stratification steepens the wave characteristics. Over a broad range in depth and along the canyon axis, they are nearly equal to the thalweg slope. It is therefore possible that the observed lack of down-canyon fluxes during this period is because the incident internal tide is more effectively dissipated owing to the near-critical slope. Dissipation is indeed greater during the last spring tide, but not during the second and only marginally during the third (Fig. 17c). Since we attribute much of the turbulence at MP2 to likely lee waves rather than critical-slope interactions, this may be a coincidence. It is possible that critical-slope dissipation occurs up canyon from our observations.

This analysis is therefore at least consistent with greater reflection leading to the down-canyon fluxes during the first period. On the other hand, the overall net up-canyon flux is similar during all four spring tides, with the first one showing greater energy (Fig. 11). This would suggest instead that the stratification in the first period leads to greater up-canyon generation, which would in turn presumably lead to greater dissipation during that period, contrary to observed. More observations and/or high-resolution, three-dimensional modeling are needed to distinguish between these two different explanations.

Our observations have several important implications for modeling internal tides incident on topography in coastal regions and for understanding the variability of internal tides in general. The lateral differences in stratification brought on by the upwelling pose difficulties in that the stratification in the remote generation region, which is further offshore, likely differs from the stratification in the canyon, where the waves interact, reflect and dissipate. For example, assumption of a laterally constant stratification might be correct for the processes inside the canyon, but incorrect for the generation and propagation of the waves feeding the canyon from remote generation sites.

These data show one more example of the variability in internal tides. Stratification has here been demonstrated to alter the structure of the wave field in a submarine canyon. Sheared mesoscale flows, not considered here, likely also contribute by modifying the modal shapes and even leading to critical layers as described by the Taylor–Goldstein equation. The observed changes in the phasing and magnitude of the dissipation suggest that these processes could influence the patterns and magnitude of dissipation in general.

Therefore, the list of potential feedbacks between internal tides and their forcing mechanisms is growing long. The generation process itself has been demonstrated to be strongly sensitive to the presence and phasing of remotely-incident internal tides (Kelly and Nash 2010). Reflection depends not only on stratification, as suggested here, but also on the modal content and phasing of the incident internal tide (Klymak et al. 2011). Finally, the internal tide appears able to affect the barotropic tide itself via its alteration of the pressure gradients, as argued in Carter (2010). This suggestion is supported here by the dissimilarity in the spring-neap cycles of barotropic sea level and currents, with the latter greater during periods of greater baroclinic energy (Fig. 14). For accurate global maps of internal tides, it may be necessary to properly account for all of these processes.

7. Conclusions

We have presented two-month, nearly-full-depth moored observations of internal tides and their breaking in the upper MSC. Our observations of net up-canyon flux and strong spring-neap cycles in energy and flux are in agreement with past studies. The current work focuses on the effects on the baroclinic signals and their dissipation associated with marked changes in the ocean stratification due to the onset of springtime upwelling-favorable winds. Our major conclusions include the following.

  • The thermocline shoals from 100 to 40 m with the onset of upwelling favorable winds during our observations. The associated changes in stratification are substantial enough to necessitate inclusion of time-varying stratification in calculations of potential energy, energy flux. The modal shapes and the distribution of energy and flux among them are also affected.
  • Because of these changes in stratification, the internal tide field changes from a partly-standing wave during the first period (yearday 48–70) to a more progressive wave during the second period (yearday 70–106).
  • The dissipation rate and diapycnal diffusivity are bottom intensified with a decay scale of 50–150 m. The decay scale shows a spring-neap cycle in phase with energy and flux, with depth-integrated dissipation about 3 times greater in the last spring tide than in the first.
  • Dissipation at MP2, which sits near the top of a submarine ridge near the Gooseneck Meander, appears tied to a breaking lee wave associated with the baroclinic flow over the ridge. However, the phasing of the dissipation relative to the baroclinic motions changes markedly between the first spring tide and the successive ones, apparently indicating that the lee-wave response may be altered in association with the changed stratification.

Acknowledgments

This work was supported by NSF through Grants OCE 0751226 and 0751420. We are grateful to caption Rick Verlini, marine technician Daryl Swensen and the entire crew of R/V Welcoma for their expertise and hard work. We are grateful to Paul Aguilar, Eric Boget, Andrew Cookson, John Mickett, and David Winkel for their skill in designing, deploying, and recovering the moorings. Discussions with Rob Hall and Danielle Wain were very helpful.

APPENDIX

Errors in Flux and Energy

Estimates of energy and energy flux are notoriously sensitive to gaps in the water column coverage. With full-depth data, baroclinic pressure can be unambiguously determined and the resulting profiles simply integrated. With less than perfect water column coverage, the calculation is done by projecting onto modes (Alford 2003), but the surface intensification of the pressure and velocity modes for typical ocean profiles of stratification makes this method particularly sensitive to gaps at the surface (Nash et al. 2005). The problem is less severe for displacement modes, which decrease to zero at the surface.

Here we take advantage of the near full-column coverage at MP2 (Fig. A1, left panels) to directly assess the errors associated with modal fits and interpolation through the gaps. We then demonstrate the degree to which the errors increase at the moorings with less coverage, starting with MP3 (Fig. A1, right panels) and then moving to the ADCP moorings (Fig. A2).

Fig. A1.
Fig. A1.

Energy and flux errors due to data gaps at MP2 and MP3. (a)–(d) Vertical profiles of u, η variance at (a),(b) MP2 and (c),(d) MP3. Gaps are shown in red. (e) APE, (g) HKE, and (i) flux magnitude at MP2 obtained from both the raw and filled data. (f),(h),(j) As in (e),(g),(i) but for MP3.

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

Fig. A2.
Fig. A2.

Comparison of depth-averaged HKE computed from modal fits (colors) and direct integration (black) at the ADCP moorings.

Citation: Journal of Physical Oceanography 42, 12; 10.1175/JPO-D-12-045.1

The profiles of displacement and velocity variance and the coverage for each quantity are indicated in Fig. A1 at top. At MP2, the vertical gaps are small enough that 10 modes can be reliably fit. However, the first few modes dominate (see Fig. 13). As a result, time series of APE, HKE, and flux magnitude from three and ten modes agree nearly perfectly (Figs. A1e,g,i, red and blue), and interpolation through the gaps makes no difference (dashed lines). The direct depth integral of APE (e, black) matches the modally-summed quantities very well, but that of HKE and flux magnitude underestimates them by 10%–40% owing to the gaps near 40 m and the bottom. It is discouraging that even with as nearly complete coverage at MP2, the flux must still be computed with modal fits or interpolation for quantitative reliability. Still, particularly given the redness of the modal spectrum, the gaps are quite reliably filled with interpolation such that the errors in the depth-integrated quantities is only a few percent at MP2.

For MP3, the absence of the HOBO data reduces the number of displacement modes that can be fit from ten to three, as seen by the unstable solutions for ten modes (f, blue). Depth-integrated APE agrees very well with the sum of modes 1–3, except for two periods. Flux is again underestimated by a slightly larger amount owing to the relatively larger gaps for displacement.

The gaps at the ADCP moorings (~40-m gap at the surface and ~20-m gap at the bottom, account for 10%–20% of the water column; Table 1) are substantially greater, leading to larger errors (Fig. A2). In the first place, only three or four modes can be stably fit compared to ten modes for MP2. More troublesome, the degree of disagreement among the modes varies in time as the modal shapes and the partition of energy among them changes with the stratification. Errors are worst during the periods of rapid change (yearday 65–75 and 90–95). In general, the directly depth-integrated HKE underestimates the modally summed quantities by ~20%, again owing to the gap at the surface. Based on the differences between the various curves, we estimate an uncertainty of about 20% for HKE determined from the ADCP moorings, recognizing that errors can be greater during rapidly changing stratification.

REFERENCES

  • Alford, M. H., 2003: Redistribution of energy available for ocean mixing by long-range propagation of internal waves. Nature, 423, 159162.

    • Search Google Scholar
    • Export Citation
  • Alford, M. H., 2010: Sustained, full-water-column observations of internal waves and mixing near Mendocino Escarpment. J. Phys. Oceanogr., 40, 26432660.

    • Search Google Scholar
    • Export Citation
  • Alford, M. H., , and Z. Zhao, 2007a: Global patterns of low-mode internal-wave propagation. Part I: Energy and energy flux. J. Phys. Oceanogr., 37, 18291848.

    • Search Google Scholar
    • Export Citation
  • Alford, M. H., , and Z. Zhao, 2007b: Global patterns of low-mode internal-wave propagation. Part II: Group velocity. J. Phys. Oceanogr., 37, 18491858.

    • Search Google Scholar
    • Export Citation
  • Alford, M. H., , M. C. Gregg, , and M. A. Merrifield, 2006: Structure, propagation and mixing of energetic baronlinic tides in Mamala Bay, Oahu, Hawaii. J. Phys. Oceanogr., 36, 9971018.

    • Search Google Scholar
    • Export Citation
  • Alford, M. H., and Coauthors, 2011: Energy flux and dissipation in Luzon Strait: Two tales of two ridges. J. Phys. Oceanogr., 41, 22112222.

    • Search Google Scholar
    • Export Citation
  • Buijsman, M. C., , S. Legg, , and J. Klymak, 2012: Double-ridge internal tide interference and its effect on dissipation in Luzon Strait. J. Phys. Oceanogr., 42, 13371356.

    • Search Google Scholar
    • Export Citation
  • Cairns, J. L., , and G. O. Williams, 1976: Internal wave observations from a midwater float, 2. J. Geophys. Res., 81, 19431950.

  • Carter, G. S., 2010: Barotropic and baroclinic M2 tides in the Monterey Bay region. J. Phys. Oceanogr., 40, 17661783.

  • Carter, G. S., , and M. C. Gregg, 2002: Intense, variable mixing near the head of Monterey submarine canyon. J. Phys. Oceanogr., 32, 31453165.

    • Search Google Scholar
    • Export Citation
  • Carter, G. S., , M. C. Gregg, , and R.-C. Lien, 2005: Internal waves, solitary-like waves, and mixing on the Monterey Bay shelf. Cont. Shelf Res., 25, 14991520.

    • Search Google Scholar
    • Export Citation
  • Dale, A. C., , J. M. Huthnance, , and T. J. Sherwin, 2001: Coastal-trapped waves and tides at near-inertial frequencies. J. Phys. Oceanogr., 31, 29582970.

    • Search Google Scholar
    • Export Citation
  • Dillon, T. M., 1982: Vertical overturns: A comparison of Thorpe and Ozmidov length scales. J. Geophys. Res., 87, 96019613.

  • Doherty, K. W., , D. E. Frye, , S. P. Liberatore, , and J. M. Toole, 1999: A moored profiling instrument. J. Atmos. Oceanic Technol., 16, 18161829.

    • Search Google Scholar
    • Export Citation
  • Eriksen, C. C., 1982: Observations of internal wave reflection off sloping bottoms. J. Geophys. Res., 87, 525538.

  • Galbraith, P. S., , and D. E. Kelley, 1996: Identifying overturns in CTD profiles. J. Atmos. Oceanic Technol., 13, 688702.

  • Gardner, W. D., 1989: Periodic resuspension in Baltimore Canyon by focusing of internal waves. J. Geophys. Res., 94, 18 18518 194.

  • Garrett, C., , and W. H. Munk, 1975: Space-time scales of internal waves: A progress report. J. Geophys. Res., 80, 291297.

  • Gill, A. E., 1982: Atmosphere-Ocean Dynamics. Academic Press, 662 pp.

  • Gonella, J., 1972: A rotary-component method for analysing meteorological and oceanographic vector time series. Deep-Sea Res., 19, 833846, doi:10.1016/0011-7471(72)90002-2.

    • Search Google Scholar
    • Export Citation
  • Gordon, R. L., , and N. F. Marshall, 1976: Submarine canyon internal wave traps? Geophys. Res. Lett., 3, 622624.

  • Gregg, M. C., , G. S. Carter, , and E. Kunze, 2005: Corrigendum. J. Phys. Oceanogr., 35, 17121715.

  • Gregg, M. C., , R. A. Hall, , G. S. Carter, , M. H. Alford, , R.-C. Lien, , D. P. Winkel, , and D. J. Wain, 2011: Flow and mixing in Ascension, a steep, narrow canyon. J. Geophys. Res.,116, C07016, doi:10.1029/2010JC006610.

  • Hall, P., , and A. M. Davies, 2007: Internal tide modeling and the influence of wind effects. Cont. Shelf Res., 27, 13571377, doi:10.1016/j.csr.2006.09.008.

    • Search Google Scholar
    • Export Citation
  • Hall, R. A., , and G. S. Carter, 2011: Internal tides in Monterey Submarine Canyon. J. Phys. Oceanogr., 41, 186204.

  • Hickey, B. M., 1995: Coastal submarine canyons. Topographic Interactions in the Ocean: Proc. ‘Aha Huliko‘a Hawaiian Winter Workshop, Honolulu, HI, University of Hawaii at Manoa, 95–110.

  • Hotchkiss, F. S., , and C. Wunsch, 1982: Internal waves in Hudson Canyon with possible geological implications. Deep-Sea Res., 29, 415442.

    • Search Google Scholar
    • Export Citation
  • Hunkins, K., 1988: Mean and tidal currents in Baltimore Canyon. J. Geophys. Res., 93, 69176929.

  • Jachec, S. M., , O. B. Fringer, , M. G. Gerritsen, , and R. L. Street, 2006: Numerical simulation of internal tides and the resulting energetics within Monterey Bay and the surrounding area. Geophys. Res. Lett.,33, L12605, doi:10.1029/2006GL026314.

  • Johnston, T. M. S., , D. L. Rudnick, , G. S. Carter, , R. E. Todd, , and S. T. Cole, 2011: Internal tidal beams and mixing near Monterey Bay. J. Geophys. Res., 116, C03017, doi:10.1029/2010JC006592.

    • Search Google Scholar
    • Export Citation
  • Kang, D., , and O. B. Fringer, 2012: Energetics of barotropic and baroclinic tides in the Monterey Bay area. J. Phys. Oceanogr., 42, 272290.

    • Search Google Scholar
    • Export Citation
  • Kelly, S. M., , and J. D. Nash, 2010: Internal-tide generation and destruction by shoaling internal tides. Geophys. Res. Lett., 37, L23611, doi:10.1029/2010GL045598.

    • Search Google Scholar
    • Export Citation
  • Kelly, S. M., , J. D. Nash, , M. H. Alford, , and K. I. Martini, 2012: The cascade of tidal energy from low to high modes on a continental slope. J. Phys. Oceanogr., 42, 12171232.

    • Search Google Scholar
    • Export Citation
  • Key, S. A., 1999: Internal tidal bores in the Monterey Canyon. M.S. thesis, Department of Oceanography, Naval Postgraduate School, 91 pp.

  • Klymak, J. M., , M. H. Alford, , R. Pinkel, , R.-C. Lien, , Y. J. Yang, , and T.-Y. Tang, 2011: The breaking and scattering of the internal tide on a continental slope. J. Phys. Oceanogr., 41, 926945.

    • Search Google Scholar
    • Export Citation
  • Kunze, E., , L. K. Rosenfeld, , G. S. Carter, , and M. C. Gregg, 2002: Internal waves in Monterey submarine canyon. J. Phys. Oceanogr., 32, 18901913.

    • Search Google Scholar
    • Export Citation
  • Kunze, E., , C. MacKay, , E. E. McPhee-Shaw, , K. Morrice, , J. B. Girton, , and S. R. Terker, 2012: Turbulent mixing and exchange with interior waters on sloping boundaries. J. Phys. Oceanogr., 42, 910–927.

    • Search Google Scholar
    • Export Citation
  • Kurapov, A. L., , G. D. Egbert, , J. S. Allen, , R. N. Miller, , S. Y. Erofeeva, , and P. M. Kosro, 2003: The M2 internal tide off Oregon: Inferences from data assimilation. J. Phys. Oceanogr., 33, 17331757.

    • Search Google Scholar
    • Export Citation
  • Kurapov, A. L., , J. S. Allen, , and G. D. Egbert, 2010: Combined effects of wind-driven upwelling and internal tide on the continental shelf. J. Phys. Oceanogr., 40, 737756.

    • Search Google Scholar
    • Export Citation
  • Lee, I.-H., , R.-C. Lien, , J. T. Liu, , and W.-S. Chuang, 2009: Turbulent mixing and internal tides in Gaoping (Kaoping) Submarine Canyon, Taiwan. J. Mar. Syst., 76, 383396, doi:10.1016/j.jmarsys.2007.08.005.

    • Search Google Scholar
    • Export Citation
  • Legg, S., , and J. Klymak, 2008: Internal hydraulic jumps and overturning generated by tidal flow over a tall steep ridge. J. Phys. Oceanogr., 38, 19491964.

    • Search Google Scholar
    • Export Citation
  • Lueck, R. G., , and T. R. Osborn, 1985: Turbulence measurements in a submarine canyon. Cont. Shelf Res., 4, 681698.

  • MacKinnon, J. A., , and M. C. Gregg, 2003a: Mixing on the late-summer New England shelf–solibores, shear and stratification. J. Phys. Oceanogr., 33, 14761492.

    • Search Google Scholar
    • Export Citation
  • MacKinnon, J. A., , and M. C. Gregg, 2003b: Shear and baroclinic energy flux on the summer New England shelf. J. Phys. Oceanogr., 33, 14621475.

    • Search Google Scholar
    • Export Citation
  • Martini, K. I., , M. H. Alford, , J. D. Nash, , E. Kunze, , and M. A. Merrifield, 2007: Diagnosing a partly-standing internal wave in Mamala Bay, Oahu. Geophys. Res. Lett.,34, L17604, doi:10.1029/2007GL029749.

  • Mooers, C. N. K., 1970: The interaction of an internal tide with the frontal zone in a coastal upwelling region. Ph.D. thesis, Oregon State University, 480 pp.

  • Nash, J. D., , E. Kunze, , J. M. Toole, , and R. W. Schmitt, 2004: Internal tide reflection and turbulent mixing on the continental slope. J. Phys. Oceanogr., 34, 11171134.

    • Search Google Scholar
    • Export Citation
  • Nash, J. D., , M. H. Alford, , and E. Kunze, 2005: Estimating internal wave energy fluxes in the ocean. J. Atmos. Oceanic Technol., 22, 15511570.

    • Search Google Scholar
    • Export Citation
  • Osborne, J. J., , A. L. Kurapov, , G. D. Egbert, , and P. M. Kosro, 2011: Spatial and temporal variability of the M2 internal tide generation and propagation on the Oregon shelf. J. Phys. Oceanogr., 41, 20372062.

    • Search Google Scholar
    • Export Citation
  • Paduan, J. D., , and L. K. Rosenfeld, 1996: Remotely sensed surface currents in Monterey Bay from shore-based HF radar (coastal ocean dynamics application radar). J. Geophys. Res., 101 (C9), 20 66920 686.

    • Search Google Scholar
    • Export Citation
  • Paull, C. K., , P. Mitts, , W. Ussler III, , R. Keaten, , and H. G. Greene, 2005: Trail of sand in upper Monterey Canyon: Offshore California. Geol. Soc. Amer. Bull., 117, 11341145, doi:10.1130/B25390.1.

    • Search Google Scholar
    • Export Citation
  • Pawlowicz, R., , B. Beardsley, , and S. Lentz, 2002: Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE. Comput. Geosci., 28, 929937.

    • Search Google Scholar
    • Export Citation
  • Pedlosky, J., 2003: Waves in the Ocean and Atmosphere: Introduction to Wave Dynamics. Springer, 268 pp.

  • Petruncio, E. T., , L. K. Rosenfeld, , and J. D. Paduan, 1998: Observations of the internal tide in Monterey Canyon. J. Phys. Oceanogr., 28, 18731903.

    • Search Google Scholar
    • Export Citation
  • Petruncio, E. T., , J. D. Paduan, , and L. K. Rosenfeld, 2002: Numerical simulations of the internal tide in a submarine canyon. Ocean Modell., 4 (3–4), 221248, doi:10.1016/S1463-5003(02)00002-1.

    • Search Google Scholar
    • Export Citation
  • Rainville, L., , T. M. S. Johnston, , G. S. Carter, , M. A. Merrifield, , R. Pinkel, , P. F. Worcester, , and B. D. Dushaw, 2010: Interference pattern and propagation of the M2 internal tide south of the Hawaiian Ridge. J. Phys. Oceanogr., 40, 311325.

    • Search Google Scholar
    • Export Citation
  • Ramp, S. R., , J. D. Paduan, , I. Shulman, , J. Kindle, , F. L. Bahr, , and F. Chavez, 2005: Observations of upwelling and relaxation events in the northern Monterey Bay during August 2000. J. Geophys. Res.,110, C07013, doi:10.1029/2004JC002538.

  • Rosenfeld, L. K., , F. B. Schwing, , N. Garfield, , and D. E. Tracy, 1994: Bifurcated flow from an upwelling center: a cold water source for Monterey Bay. Cont. Shelf Res., 14, 931964, doi:10.1016/0278-4343(94)90058-2.

    • Search Google Scholar
    • Export Citation
  • Shea, R. E., , and W. W. Broenkow, 1982: The role of internal tides in nutrient enrichment of Monterey Bay, California. Estuarine Coastal Shelf Sci., 15, 5766.

    • Search Google Scholar
    • Export Citation
  • Slinn, D., , and M. Levine, 2003: Modeling internal tides and mixing over ocean ridges. Dynamics of Oceanic Internal Gravity Waves, II: Proc. ‘Aha Huliko‘a Hawaiian Winter Workshop, Honolulu, HI, University of Hawaii at Manoa, 59–68.

  • Swart, N. C., , S. E. Allen, , and B. J. W. Greenan, 2011: Resonant amplification of subinertial tides in a submarine canyon. J. Geophys. Res.,116, C09001, doi:10.1029/2011JC006990.

  • Thorpe, S., 1977: Turbulence and mixing in a Scottish loch. Philos. Trans. Roy. Soc. London, 286A, 125181.

  • Wunsch, C., , and S. Webb, 1979: The climatology of deep ocean internal waves. J. Phys. Oceanogr., 9, 235243.

  • Xu, J. P., , and M. A. Noble, 2009: Currents in Monterey Submarine Canyon. J. Geophys. Res.,114, C03004, doi:10.1029/2008JC004992.

  • Zhao, Z., , M. H. Alford, , J. A. MacKinnon, , and R. Pinkel, 2010: Long-range propagation of the semidiurnal internal tides from the Hawaiian Ridge. J. Phys. Oceanogr., 40, 713736.

    • Search Google Scholar
    • Export Citation
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