Energy Fluxes in Coastal Trapped Waves

R. C. Musgrave Woods Hole Oceanographic Institution, Woods Hole, Massachusetts

Search for other papers by R. C. Musgrave in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

The calculation of energy flux in coastal trapped wave modes is reviewed in the context of tidal energy pathways near the coast. The significant barotropic pressures and currents associated with coastal trapped wave modes mean that large errors in estimating the wave flux are incurred if only the baroclinic component is considered. A specific example is given showing that baroclinic flux constitutes only 10% of the flux in a mode-1 wave for a reasonable choice of stratification and bathymetry. The interpretation of baroclinic energy flux and barotropic-to-baroclinic conversion at the coast is discussed: in contrast to the open ocean, estimates of baroclinic energy flux do not represent a wave energy flux; neither does conversion represent the scattering of energy from the tidal Kelvin wave to higher modes.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: R. C. Musgrave, rmusgrave@whoi.edu

Abstract

The calculation of energy flux in coastal trapped wave modes is reviewed in the context of tidal energy pathways near the coast. The significant barotropic pressures and currents associated with coastal trapped wave modes mean that large errors in estimating the wave flux are incurred if only the baroclinic component is considered. A specific example is given showing that baroclinic flux constitutes only 10% of the flux in a mode-1 wave for a reasonable choice of stratification and bathymetry. The interpretation of baroclinic energy flux and barotropic-to-baroclinic conversion at the coast is discussed: in contrast to the open ocean, estimates of baroclinic energy flux do not represent a wave energy flux; neither does conversion represent the scattering of energy from the tidal Kelvin wave to higher modes.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: R. C. Musgrave, rmusgrave@whoi.edu
Save
  • Adcroft, A., C. Hill, and J. Marshall, 1997: Representation of topography by shaved cells in a height coordinate ocean model. Mon. Wea. Rev., 125, 22932315, https://doi.org/10.1175/1520-0493(1997)125<2293:ROTBSC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brink, K. H., 1989: Energy conservation in coastal-trapped wave calculations. J. Phys. Oceanogr., 19, 10111016, https://doi.org/10.1175/1520-0485(1989)019<1011:ECICTW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brink, K. H., 2006: Coastal-trapped waves with finite bottom friction. Dyn. Atmos. Oceans, 41, 172190, https://doi.org/10.1016/j.dynatmoce.2006.05.001.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Carter, G. S., and Coauthors, 2008: Energetics of M2 barotropic-to-baroclinic tidal conversion at the Hawaiian Islands. J. Phys. Oceanogr., 38, 22052223, https://doi.org/10.1175/2008JPO3860.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cartwright, D. E., 1969: Extraordinary tidal currents near St Kilda. Nature, 223, 928932, https://doi.org/10.1038/223928a0.

  • Chapman, D. C., 1983: On the influence of stratification and continental shelf and slope topography on the dispersion of subinertial coastally trapped waves. J. Phys. Oceanogr., 13, 16411652, https://doi.org/10.1175/1520-0485(1983)013<1641:OTIOSA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Clarke, A. J., 1977: Observational and numerical evidence for wind-forced coastal trapped long waves. J. Phys. Oceanogr., 7, 231247, https://doi.org/10.1175/1520-0485(1977)007<0231:OANEFW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Crawford, W. R., 1984: Energy flux and generation of diurnal shelf waves along Vancouver Island. J. Phys. Oceanogr., 14, 16001607, https://doi.org/10.1175/1520-0485(1984)014<1600:EFAGOD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dale, A. C., and T. J. Sherwin, 1996: The extension of baroclinic coastal-trapped wave theory to superinertial frequencies. J. Phys. Oceanogr., 26, 23052315, https://doi.org/10.1175/1520-0485(1996)026<2305:TEOBCT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Egbert, G., and R. D. Ray, 2000: Significant dissipation of tidal energy in the deep ocean inferred from satellite altimiter data. Nature, 405, 775778, https://doi.org/10.1038/35015531.

    • Search Google Scholar
    • Export Citation
  • Fer, I., M. Müller, and A. K. Peterson, 2015: Tidal forcing, energetics, and mixing near the Yermak Plateau. Ocean Sci., 11, 287304, https://doi.org/10.5194/os-11-287-2015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hughes, K. G., and J. M. Klymak, 2019: Tidal conversion and dissipation at steep topography in a channel poleward of the critical latitude. J. Phys. Oceanogr., 49, 12691291, https://doi.org/10.1175/JPO-D-18-0132.1.

    • Search Google Scholar
    • Export Citation
  • Huthnance, J. M., 1978: On coastal trapped waves: Analysis and numerical calculation by inverse iteration. J. Phys. Oceanogr., 8, 7492, https://doi.org/10.1175/1520-0485(1978)008<0074:OCTWAA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jeffreys, H., 1921: Tidal friction in shallow seas. Philos. Trans. Roy. Soc. London, 221A, 239264, https://doi.org/10.1098/rsta.1921.0008.

    • 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, https://doi.org/10.1175/JPO-D-11-039.1.

    • Search Google Scholar
    • Export Citation
  • Kelly, S. M., 2016: The vertical mode decomposition of surface and internal tides in the presence of a free surface and arbitrary topography. J. Phys. Oceanogr., 46, 37773788, https://doi.org/10.1175/JPO-D-16-0131.1.

    • Search Google Scholar
    • Export Citation
  • Klymak, J. M., H. L. Simmons, D. Braznikov, S. Kelly, J. A. MacKinnon, M. H. Alford, R. Pinkel, and J. D. Nash, 2016: Reflection of linear internal tides from realistic topography: The Tasman continental slope. J. Phys. Oceanogr., 46, 33213337, https://doi.org/10.1175/JPO-D-16-0061.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, Z., J.-S. von Storch, and M. Müller, 2017: The K1 internal tide simulated by a 1/10° OGCM. Ocean Modell., 113, 145156, https://doi.org/10.1016/j.ocemod.2017.04.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, J., A. Adcroft, C. Hill, L. Perelman, and C. Heisey, 1997: A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. J. Geophys. Res., 102, 57535766, https://doi.org/10.1029/96JC02775.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Masunaga, E., O. B. Fringer, Y. Kitade, H. Yamazaki, and S. M. Gallager, 2017: Dynamics and energetics of trapped diurnal internal Kelvin waves around a midlatitude island. J. Phys. Oceanogr., 47, 24792498, https://doi.org/10.1175/JPO-D-16-0167.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Müller, M., 2013: On the space-and time-dependence of barotropic-to-baroclinic tidal energy conversion. Ocean Modell., 72, 242252, https://doi.org/10.1016/j.ocemod.2013.09.007.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Musgrave, R. C., J. A. MacKinnon, R. Pinkel, A. F. Waterhouse, J. Nash, and S. M. Kelly, 2017: The influence of subinertial internal tides on near-topographic turbulence at the Mendocino Ridge: Observations and modeling. J. Phys. Oceanogr., 47, 21392154, https://doi.org/10.1175/JPO-D-16-0278.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nash, J. D., M. H. Alford, and E. Kunze, 2005: On estimating internal-wave energy fluxes in the ocean. J. Atmos. Oceanic Technol., 22, 15511570, https://doi.org/10.1175/JTECH1784.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Niwa, Y., and T. Hibiya, 2011: Estimation of baroclinic tide energy available for deep ocean mixing based on three-dimensional global numerical simulations. J. Oceanogr., 67, 493502, https://doi.org/10.1007/s10872-011-0052-1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Salmon, R., 1998: Lectures on Geophysical Fluid Dynamics. Oxford University Press, 400 pp.

    • Crossref
    • Export Citation
  • Tanaka, Y., T. Hibiya, Y. Niwa, and N. Iwamae, 2010: Numerical study of K1 internal tides in the Kuril straits. J. Geophys. Res., 115, C09016, https://doi.org/10.1029/2009JC005903.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tanaka, T., I. Yasuda, Y. Tanaka, and G. S. Carter, 2013: Numerical study on tidal mixing along the shelf break in the Green Belt in the southeastern Bering Sea. J. Geophys. Res. Oceans, 118, 65256542, https://doi.org/10.1002/2013JC009113.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Taylor, G. I., 1919: Tidal friction in the Irish Sea. Proc. Roy. Soc. London, 96A, 330, https://doi.org/10.1098/rspa.1919.0059.

  • Wang, D.-P., and C. N. Mooers, 1976: Coastal-trapped waves in a continuously stratified ocean. J. Phys. Oceanogr., 6, 853863, https://doi.org/10.1175/1520-0485(1976)006<0853:CTWIAC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 558 132 10
PDF Downloads 559 142 11