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Internal tide generation by arbitrary two-dimensional topography

Published online by Cambridge University Press:  30 June 2010

PAULA ECHEVERRI  and
THOMAS PEACOCK
PAULA ECHEVERRI*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
THOMAS PEACOCK
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
*
†Email address for correspondence: pauleche@gmail.com
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Abstract

To date, analytical models of internal tide generation by two-dimensional ridges have considered only idealized shapes. Here, we advance the Green function approach to address the generation of internal tides by two-dimensional topography of arbitrary shape, employing the Wentzel-Kramers-Brillouin (WKB) approximation to consider the impact of non-uniform stratifications. This allows for a more accurate analytical estimation of tidal conversion rates. Studies of single and double ridges reveal that the conversion rate and the nature of the radiated internal tide can be sensitive to the topographic shape, particularly around criticality and when there is interference between wave fields generated by neighbouring ridges. The method is then applied to the study of two important internal tide generation sites, the Hawaiian and Luzon Ridges, where it captures key features of the generation process.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows Geophysical and Geological Flows: Topographic effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 659 , 25 September 2010 , pp. 247 - 266
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Althaus, A. M., Kunze, E. & Sanford, T. B. 2003 Internal tide radiation from Mendocino Escarpment. J. Phys. Oceanogr. 33, 1510–1527.2.0.CO;2>CrossRefGoogle Scholar
Baines, P. G. 1973 The generation of internal tides by flat-bump topography. Deep Sea Res. 20, 179–205.Google Scholar
Baines, P. G. 1982 On internal tide generation models. Deep Sea Res. 29, 307–338.CrossRefGoogle Scholar
Balmforth, N. J., Ierley, G. R. & Young, W. R. 2002 Tidal conversion by subcritical topography. J. Phys. Oceanogr. 32, 2900–2914.2.0.CO;2>CrossRefGoogle Scholar
Balmforth, N. J. & Peacock, T. 2009 Tidal conversion by supercritical topography. J. Phys. Oceanogr. 39, 1965–1974.CrossRefGoogle Scholar
Becker, J. J., Sandwell, D. T., Smith, W. H. F., Braud, J., Binder, B., Depner, J., Fabre, D., Factor, J., Ingalls, S., Kim, S.-H., Ladner, R., Marks, K., Nelson, S., Pharaoh, A., Sharman, G., Trimmer, R., vonRosenburg, J., Wallace, G. & Weatherall, P. 2009 Global bathymetry and elevation data at 30 arc seconds resolution: SRTM30_PLUS. Marine Geodesy 32 (4), 355–371.CrossRefGoogle Scholar
Bell, T. H. 1975 Lee waves in stratified flows with simple harmonic time dependence. J. Fluid Mech. 67, 705–722.CrossRefGoogle Scholar
Carter, G. S., Merrifield, M. A., Becker, J. M., Katsumata, K., Gregg, M. C., Luther, D. S., Levine, M. D., Boyd, T. J. & Firing, Y. L. 2008 Energetics of M2 barotropic-to-baroclinic tidal conversion at the Hawaiian islands. J. Phys. Oceanogr. 38, 2205–2223.CrossRefGoogle Scholar
Chao, S. Y., Ko, D. S., Lien, R. C. & Shaw, P. T. 2007 Assessing the west ridge of Luzon Strait as an internal wave mediator. J. Oceanogr. 63, 897–911.CrossRefGoogle Scholar
Echeverri, P., Flynn, M. R., Winters, K. B. & Peacock, T. 2009 Low-mode internal tide generation by topography: an experimental and numerical investigation. J. Fluid Mech. 636, 91–108.CrossRefGoogle Scholar
Echeverri, P., Yokossi, T., Balmforth, N. J. & Peacock, T. 2010 Internal tide attractors in double ridges. J. Fluid Mech. (submitted).Google Scholar
Egbert, G. D. & Ray, R. D. 2000 Significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data. Nature 405, 775–778.CrossRefGoogle ScholarPubMed
Farmer, D. M., Li, Q. & Park, J. 2009 Internal wave observations in the South China Sea: the role of rotation and nonlinearity. Atmos. Ocean 47 (4), 267–280.CrossRefGoogle Scholar
Garrett, C. & Kunze, E. 2007 Internal tide generation in the deep ocean. Annu. Rev. Fluid Mech. 39, 57–87.CrossRefGoogle Scholar
Griffiths, S. D. & Grimshaw, R. H. J. 2007 Internal tide generation at the continental shelf modeled using a modal decomposition: two-dimensional results. J. Phys. Oceanogr. 37, 428–451.CrossRefGoogle Scholar
Grisouard, N., Staquet, C. & Pairaud, I. 2008 Numerical simulation of a two-dimensional internal wave attractor. J. Fluid Mech. 614, 1–14.CrossRefGoogle Scholar
Hawaii Mapping Research Group 2009 Main Hawaiian Islands multibeam synthesis. http://www.soest.hawaii.edu/HMRG/Multibeam/index.php.Google Scholar
Hawaiian Ocean Time-series 2009 http://hahana.soest.hawaii.edu/hot/hot_jgofs.html.Google Scholar
Hazewinkel, J., Van Breevoort, P., Dalziel, S. B. & Maas, L. R. M. 2008 Observations on the wavenumber spectrum and evolution of an internal wave attractor. J. Fluid Mech. 598, 373–382.CrossRefGoogle Scholar
Jan, S., Lien, R. C. & Ting, C. H. 2008 Numerical study of baroclinic tides in Luzon Strait. J. Oceanogr. 64, 789–802.CrossRefGoogle Scholar
Khatiwala, S. 2003 Generation of internal tides in an ocean of finite depth: analytical and numerical calculations. Deep Sea Res. 50, 3–21.CrossRefGoogle Scholar
Klymak, J. M., Moum, J. N., Nash, J. D., Kunze, E., Griton, J. B., Carter, G. S., Lee, C. M., Sanford, T. B. & Gregg, M. C. 2006 An estimate of tidal energy lost to turbulence at the Hawaiian Ridge. J. Phys. Oceanogr. 36, 1148–1164.CrossRefGoogle Scholar
Klymak, J. M., Pinkel, R. & Rainville, L. 2008 Direct breaking of the internal tide near topography: Kaena Ridge, Hawaii. J. Phys. Oceanogr. 38 (2), 380–399.CrossRefGoogle Scholar
Lee, C. M., Kunze, E., Sanford, T. B., Nash, J. D., Merrifield, M. A. & Holloway, P. E. 2006 Internal tides and turbulence along the 3000-m isobath of the Hawaiian ridge. J. Phys. Oceanogr. 36, 1165–1183.CrossRefGoogle Scholar
Llewellyn Smith, S. G. & Young, W. R. 2002 Conversion of the barotropic tide. J. Phys. Oceanogr. 32, 1554–1566.2.0.CO;2>CrossRefGoogle Scholar
Llewellyn Smith, S. G. & Young, W. R. 2003 Tidal conversion at a very steep ridge. J. Fluid Mech. 495, 175–191.CrossRefGoogle Scholar
Maas, L. R. M., Benielli, D., Sommeria, J. & Lam, F. P. A. 1997 Observation of an internal wave attractor in a confined stably-stratified fluid. Nature 388, 557–561.CrossRefGoogle Scholar
Merrifield, M. A. & Holloway, P. E. 2002 Model estimates of M2 internal tide energetics at the Hawaiian ridge. J. Geophys. Res. 107 (C8), 3179–3190.CrossRefGoogle Scholar
Nash, J. D., Kunze, E., Lee, C. M. & Sanford, T. B. 2006 Structure of the baroclinic tide generated at Kaena Ridge, Hawaii. J. Phys. Oceanogr. 36, 1123–1135.CrossRefGoogle Scholar
National Geophysical Data Center, National Oceanic and Atmospheric Administration, U.S. Department of Commerce 2006 2-minute gridded global relief data (ETOPO2v2). http://www.ngdc.noaa.gov/mgg/fliers/06mgg01.html.Google Scholar
Niwa, Y. & Hibiya, T. 2004 Three-dimensional numerical simulation of M2 internal tides in the East China Sea. J. Geophys. Res. 109, C04027.CrossRefGoogle Scholar
Nycander, J. 2005 Generation of internal waves in the deep ocean. J. Geophys. Res. 110, C10028.CrossRefGoogle Scholar
Nycander, J. 2006 Tidal generation of internal waves from a periodic array of steep ridges. J. Fluid Mech. 567, 415–432.CrossRefGoogle Scholar
Pétrélis, F., Llewellyn Smith, S. G. & Young, W. R. 2006 Tidal conversion at a submarine ridge. J. Phys. Oceanogr. 36, 1053–1071.CrossRefGoogle Scholar
Rainville, L. & Pinkel, R. 2006 Baroclinic energy flux at the Hawaiian ridge: observations from the R/P FLIP. J. Phys. Oceanogr. 36, 1104–1122.CrossRefGoogle Scholar
Ray, R. D. & Mitchum, G. T. 1997 Surface manifestation of internal tides in the deep ocean: Observations from altimetry and island gauges. Prog. Oceanogr. 40, 135–162.CrossRefGoogle Scholar
Robinson, R. M. 1969 The effects of a barrier on internal waves. Deep Sea Res. 16, 421–429.Google Scholar
Rudnick, D. L., Boyd, T. J., Brainard, R. E., Carter, G. S., Egbert, G. D., Gregg, M. C., Holloway, P. E., Klymak, J. M., Kunze, E., Lee, C. M., Levine, M. D., Luther, D. S., Martin, J. P., Merrifield, M. A., Moum, J. N., Nash, J. D., Pinkel, R., Rainville, L. & Sanford, T. B. 2003 From tides to mixing along the Hawaiian ridge. Science 301, 355–357.CrossRefGoogle ScholarPubMed
Simmons, H. L., Hallberg, R. W. & Arbic, B. K. 2004 Internal wave generation in a global baroclinic tide model. Deep Sea Res. 51, 3043–3068.CrossRefGoogle Scholar
St Laurent, L., Stringer, S., Garrett, C. & Perrault-Joncas, D. 2003 The generation of internal tides at abrupt topography. Deep Sea Res. 50 (8), 987–1003.CrossRefGoogle Scholar
St Laurent, L. C. & Nash, J. D. 2004 An examination of the radiative and dissipative properties of deep ocean internal tides. Deep Sea Res. 51, 3029–3042.CrossRefGoogle Scholar