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Can barotropic tide–eddy interactions excite internal waves?

  • M.-P. Lelong (a1) and E. Kunze (a2)

Abstract

The interaction of barotropic tidal currents and baroclinic geostrophic eddies is considered theoretically and numerically to determine whether energy can be transferred to an internal wave field by this process. The eddy field evolves independently of the tide, suggesting that it acts catalytically in facilitating energy transfer from the barotropic tide to the internal wave field, without exchanging energy with the other flow components. The interaction is identically zero and no waves are generated when the barotropic tidal current is horizontally uniform. Optimal internal wave generation occurs when the scales of tide and eddy fields satisfy resonant conditions. The most efficient generation is found if the tidal current horizontal scale is comparable to that of the eddies, with a weak maximum when the scales differ by a factor of two. Thus, this process is not an effective mechanism for internal wave excitation in the deep ocean, where tidal current scales are much larger than those of eddies, but it may provide an additional source of internal waves in coastal areas where horizontal modulation of the tide by topography can be significant.

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Copyright

The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution-NonCommercial-ShareAlike licence . The written permission of Cambridge University Press must be obtained for commercial re-use.

Corresponding author

Email address for correspondence: pascale@nwra.com

References

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Althaus, A. M., Kunze, E. & Sanford, T. B. 2003 Internal tide radiation from Mendocino Escarpment. J. Phys. Oceanogr. 33, 15101527.
Balmforth, N. J., Ierley, G. R. & Young, W. R. 2002 Tidal conversion by subcritical topography. J. Phys. Oceanogr. 32, 29002914.
Bell, T. H. 1975 Topographically generated internal waves in the open ocean. J. Geophys. Res. 80, 320327.
Cox, C. & Sandstrom, H. 1962 Coupling of internal and surface waves in water of variable depth. J. Oceanogr. Soc. Japan 18, 499513.
Danioux, E. & Klein, P. 2008 A resonance mechanism leading to wind-forced motions with a $2f$ frequency. J. Phys. Oceanogr. 38 (10), 23222329.
Egbert, G. D. & Ray, R. 2001 Estimates of ${M}_{2} $ tidal energy dissipation from TOPEX/Poseidon altimeter data. J. Geophys. Res. 106, 22 47522 502.
Ford, R., McIntyre, M. E. & Norton, W. A. 2000 Balance and the slow quasimanifold: some explicit results. J. Atmos. Sci. 57 (9), 12361254.
Garrett, C. J. R. & Kunze, E. 2007 Internal tide generation in the deep ocean. Annu. Rev. Fluid Mech. 39, 5787.
Gill, A. E. 1982 Atmosphere–Ocean Dynamics. Academic Press.
Holloway, P. E. & Merrifield, M. A. 1999 Internal tide generation by seamounts, ridges and islands. J. Geophys. Res. 104, 25 93725 951.
Kevorkian, J. & Cole, J. D. 1981 Perturbation Methods in Applied Mathematics. Springer.
Khatiwala, S. 2003 Generation of internal tides in an ocean of finite depth: analytical and numerical calculation. Deep-Sea Res. 50, 321.
Kunze, E. 1985 Near-inertial wave propagation in geostrophic shear. J. Phys. Oceanogr. 15, 544565.
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, 11651183.
Lelong, M.-P. & Riley, J. J. 1991 Internal wave–vortical mode interactions in strongly stratified flows. J. Fluid Mech. 232, 119.
Llewellyn Smith, S. G. & Young, W. R. 2002 Conversion of the barotropic tide. J. Phys. Oceanogr. 32, 15541556.
Llewellyn Smith, S. G. & Young, W. R. 2003 Tidal conversion at a very steep ridge. J. Fluid Mech. 495, 175191.
MacCready, P. & Pawlak, G. 2001 Stratified flow along a rough slope: separation drag and wave drag. J. Phys. Oceanogr. 31, 28242839.
McComas, C. H. & Bretherton, F. P. 1977 Resonant interaction of oceanic internal waves. J. Geophys. Res. 83, 13971412.
Merrifield, M. A. & Holloway, P. E. 2002 Model estimates of M2 internal tide energetics at the Hawaiian Ridge. J. Geophys. Res. 107, 3179.
Morozov, E. G. 1995 Semidiurnal internal wave global field. Deep-Sea Res. 42, 135148.
Müller, P., Holloway, G., Henyey, F. & Pomphrey, N. 1986 Nonlinear interactions among internal gravity waves. Rev. Geophys. 24, 493536.
Nash, J. D., Kunze, E., Sanford, T. B. & Lee, C. M. 2006 Structure of the baroclinic tide generated at Kaena Ridge, Hawaii. J. Phys. Oceanogr. 36, 11231135.
Petrelis, F., Llewellyn Smith, S. G. & Young, W. R. 2006 Tidal conversion at a submarine ridge. J. Phys. Oceanogr. 36, 10531071.
Pingree, R. D., Mardell, G. T. & New, A. L. 1986 Propagation of internal tides from the upper slopes of the Bay of Biscay. Nature 321, 154158.
Pingree, R. D. & New, A. L. 1989 Downward propagation of internal tide energy into the Bay of Biscay. Deep-Sea Res. 36, 735758.
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, 135162.
Reznik, G. M., Zeitlin, V. & Ben Jelloul, M. 2001 Nonlinear theory of geostrophic adjustment. Part 1. Rotating shallow-water model. J. Fluid Mech. 445, 93120.
Rogachev, K. A. & Carmack, E. C. 2002 Evidence for the trapping and amplification of near-inertial motions in a large anticyclonic ring in the Oyashio Current. J. Oceanogr. 58, 673682.
Rogachev, K. A., Carmack, E., Miyaki, M., Thompson, R. & Yurasov, G. I. 1992 Drifting buoy in an anticyclonic eddy of the Oyashio Current. Dokl. Ross. Akad. Nauk 326, 547550.
Rogachev, K. A., Salomatin, A. S., Yusupov, V. I. & Carmack, E. C. 1996 On the internal structure of the Kuril Current anticyclonic eddies. Okeanologiya 36, 247354.
Rudnick, D. L., Boyd, T., Brainard, R. E., Carter, G. S., Egbert, G. D., Gregg, M. C., Holloway, P. E., Klymak, J., Kunze, E., Lee, C. M., Levine, M. D., Luther, D. S., Martin, J., Merrifield, M. A., Nash, J. N., Pinkel, R., Rainville, L. & Sanford, T. B. 2003 From tides to mixing along the Hawaiian Ridge. Science 301, 355357.
Simmons, H., Hallberg, R. W. & Arbic, B. K. 2004 Internal wave generation in a global baroclinic tide model. Deep-Sea Res. 51, 30433068.
St Laurent, L. C. & Garrett, C. J. R. 2002 The role of internal tides in mixing the deep ocean. J. Phys. Oceanogr. 32, 28822899.
St Laurent, L. C., Stringer, S., Garrett, C. J. R. & Perrault-Joncas, D. 2003 The generation of internal tides at abrupt topography. Deep-Sea Res. 50, 9871003.
Thorpe, S. A. 1992 The generation of internal waves by flow over the rough topography of a continental slope. Proc. R. Soc. Lond. A 439A, 115130.
Vlasenko, V., Stashchuk, N. & Hutter, K. 2005 Baroclinic Tides: Theoretical Modeling and Observational Evidence. Cambridge University Press.
Waite, M. L. & Bartello, P. 2004 Stratified turbulence dominated by vortical motion. J. Fluid Mech. 517, 281308.
Winters, K. B. & de la Fuente, A. 2012 Modelling rotating stratified flows at laboratory-scale using spectrally-based DNS. Ocean Model. 49, 4759.
Wunsch, C. 1975 Internal tides in the ocean. Rev. Geophys. Space Phys. 13, 167182.
Zeitlin, V., Reznik, G. M. & Ben Jelloul, M. 2003 Nonlinear theory of geostrophic adjustment. Part 2. Two-layer and continuously stratified primitive equations. J. Fluid Mech. 491, 207228.
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Can barotropic tide–eddy interactions excite internal waves?

  • M.-P. Lelong (a1) and E. Kunze (a2)

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