Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-24T20:16:10.405Z Has data issue: false hasContentIssue false
  • English
  • Français

Low-mode internal tide generation by topography: an experimental and numerical investigation

Published online by Cambridge University Press:  25 September 2009

PAULA ECHEVERRI ,
M. R. FLYNN ,
KRAIG B. WINTERS  and
THOMAS PEACOCK
PAULA ECHEVERRI*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
M. R. FLYNN
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
KRAIG B. WINTERS
Affiliation:
Scripps Institution of Oceanography and Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093, USA
THOMAS PEACOCK
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We analyse the low-mode structure of internal tides generated in laboratory experiments and numerical simulations by a two-dimensional ridge in a channel of finite depth. The height of the ridge is approximately half of the channel depth and the regimes considered span sub- to supercritical topography. For small tidal excursions, of the order of 1% of the topographic width, our results agree well with linear theory. For larger tidal excursions, up to 15% of the topographic width, we find that the scaled mode 1 conversion rate decreases by less than 15%, in spite of nonlinear phenomena that break down the familiar wave-beam structure and generate harmonics and inter-harmonics. Modes two and three, however, are more strongly affected. For this topographic configuration, most of the linear baroclinic energy flux is associated with the mode 1 tide, so our experiments reveal that nonlinear behaviour does not significantly affect the barotropic to baroclinic energy conversion in this regime, which is relevant to large-scale ocean ridges. This may not be the case, however, for smaller scale ridges that generate a response dominated by higher modes.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 636 , 10 October 2009 , pp. 91 - 108
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

Present address: Department of Mechanical Engineering, University of Alberta, Edmonton, AB, Canada T6G 2G8.

References

REFERENCES

Aguilar, D. A. & Sutherland, B. R. 2006 Internal wave generation from rough topography. Phys. Fluids 18, 066603.Google Scholar
Bell, T. H. 1975 Lee waves in stratified flows with simple harmonic time dependence. J. Fluid Mech. 67, 705–722.Google Scholar
Di Lorenzo, E., Young, W. R. & Llewellyn Smith, S. G. 2006 Numerical and analytical estimates of M2 tidal conversion at steep oceanic ridges. J. Phys. Oceanogr. 36, 1072–1084.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.Google Scholar
Flynn, M. R., Onu, K. & Sutherland, B. R. 2003 Internal wave generation by a vertically oscillating sphere. J. Fluid Mech. 494, 65–93.Google Scholar
Garrett, C. & Kunze, E. 2007 Internal tide generation in the deep ocean. Annu. Rev. Fluid Mech. 39, 57–87.Google Scholar
Hurley, D. G. & Keady, G. 1997 The generation of internal waves by vibrating elliptic cylinders. Part 2. Approximate viscous solution. J. Fluid Mech. 351, 119–138.CrossRefGoogle Scholar
Korobov, A. S. & Lamb, K. G. 2008 Interharmonics in internal gravity waves generated by tide-topography interaction. J. Fluid Mech. 611, 61–95.Google Scholar
Kunze, E. & Llewellyn Smith, S. G. 2004 The role of small-scale topography in turbulent mixing of the global ocean. Oceanography 17, 55–64.Google Scholar
Lamb, K. G. 2004 Nonlinear interaction among internal wave beams generated by tidal flow over supercritical topography. Geophys. Res. Lett. 31, L09313.CrossRefGoogle Scholar
Legg, S. & Huijts, K. M. H. 2006 Preliminary simulations of internal waves and mixing generated by finite amplitude tidal flow over isolated topography. Deep-Sea Res. II 53, 140–156.Google Scholar
Lighthill, M. J. 1978 Waves in Fluids. Cambridge University Press.Google Scholar
Llewellyn Smith, S. G. & Young, W. R. 2003 Tidal conversion at a very steep ridge. J. Fluid Mech. 495, 175–191.Google Scholar
Nash, J. D., Alford, M. H. & Kunze, E. 2005 Estimating internal wave energy fluxes in the ocean. J. Atmos. Ocean. Technol. 22, 1551–1570.Google Scholar
Oster, G. 1965 Density gradients. Sci. Am. 213, 70–76.Google Scholar
Peacock, T., Echeverri, P. & Balmforth, N. J. 2008 An experimental investigation of internal tide generation by two-dimensional topography. J. Phys. Oceanogr. 38, 235–242.Google Scholar
Peacock, T. & Tabaei, A. 2005 Visualization of nonlinear effects in reflecting internal wave beams. Phys. Fluids 17, 061702.CrossRefGoogle Scholar
Pétrélis, F., Llewellyn Smith, S. G. & Young, W. R. 2006 Tidal conversion at a submarine ridge. J. Phys. Oceanogr. 36, 1053–1071.Google Scholar
Ray, R. D. & Mitchum, G. T. 1997 Surface manifestation of internal tides in the deep ocean: osbservations from altimetry and island gauges. Prog. Oceanogr. 40, 135–162.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.Google Scholar
Simmons, H. L., Hallberg, R. W. & Arbic, B. K. 2004 Internal wave generation in a global baroclinic tide model. Deep-Sea Res. II 51, 3043–3068.Google Scholar
Spiegel, E. A. & Veronis, G. 1960 On the Boussinesq approximation for a compressible fluid. Astrophys. J. 131, 442–447.Google Scholar
St.Laurent, L. C. & Garrett, C. 2002 The role of internal tides in mixing the deep ocean. J. Phys. Oceanogr. 32, 2882–2899.2.0.CO;2>CrossRefGoogle Scholar
Tabaei, A., Akylas, T. R. & Lamb, K. G. 2005 Nonlinear effects in reflecting and colliding internal wave beams. J. Fluid Mech. 526, 217–243.Google Scholar
Zhang, H. P., King, B. & Swinney, H. L. 2007 Experimental study of internal gravity waves generated by supercritical topography. Phys. Fluids 19, 096602.CrossRefGoogle Scholar