Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T07:18:27.540Z Has data issue: false hasContentIssue false

Generation of internal solitary waves in a pycnocline by an internal wave beam: a numerical study

Published online by Cambridge University Press:  01 April 2011

N. GRISOUARD*
Affiliation:
Laboratoire des Écoulements Géophysiques et Industriels, UJF/CNRS/G-INP, BP 53, 38041 Grenoble CEDEX 9, France
C. STAQUET
Affiliation:
Laboratoire des Écoulements Géophysiques et Industriels, UJF/CNRS/G-INP, BP 53, 38041 Grenoble CEDEX 9, France
T. GERKEMA
Affiliation:
Royal Netherlands Institute for Sea Research, PO Box 59, 1790 AB Texel, The Netherlands
*
Email address for correspondence: grisouard@cims.nyu.edu

Abstract

Oceanic observations from western Europe and the south-western Indian ocean have provided evidence of the generation of internal solitary waves due to an internal tidal beam impinging on the pycnocline from below – a process referred to as ‘local generation’ (as opposed to the more direct generation over topography). Here we present the first direct numerical simulations of such a generation process with a fully nonlinear non-hydrostatic model for an idealised configuration. We show that, depending on the parameters, different modes can be excited and we provide examples of internal solitary waves as first, second and third modes, trapped in the pycnocline. A criterion for the selection of a particular mode is put forward, in terms of phase speeds. In addition, another simpler geometrical criterion is presented to explain the selection of modes in a more intuitive way. Finally, results are discussed and compared with the configuration of the Bay of Biscay.

Type
Papers
Copyright
Copyright © Cambridge University Press 2011

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.)

References

REFERENCES

Akylas, T. R., Grimshaw, R. H. J., Clarke, S. R. & Tabaei, A. 2007 Reflecting tidal wave beams and local generation of solitary waves in the ocean thermocline. J. Fluid Mech. 593, 297313.CrossRefGoogle Scholar
Azevedo, A., da Silva, J. C. B. & New, A. L. 2006 On the generation and propagation of internal solitary waves in the southern Bay of Biscay. Deep-Sea Res. I 53, 927941.CrossRefGoogle Scholar
Delisi, D. P. & Orlanski, I. 1975 On the role of density jumps in the reflexion and breaking of internal gravity waves. J. Fluid Mech. 69, 445464.CrossRefGoogle Scholar
Gerkema, T. 2001 Internal and interfacial tides: Beam scattering and local generation of solitary waves. J. Mar. Res. 59, 227255.CrossRefGoogle Scholar
Gerkema, T., Lam, F.-P. A. & Maas, L. R. M. 2004 Internal tides in the Bay of Biscay: Conversion rates and seasonal effects. Deep-Sea Res. II 51, 29953008.Google Scholar
Gostiaux, L. & Dauxois, T. 2007 Laboratory experiments on the generation of internal tidal beams over steep slopes. Phys. Fluids 19 (2), 028102.CrossRefGoogle Scholar
Grisouard, N. & Staquet, C. 2010 Numerical simulations of the local generation of internal solitary waves in the Bay of Biscay. Nonlinear Process. Geophys. 17, 575584.Google Scholar
Helfrich, K. R. & Melville, W. K. 2006 Long nonlinear internal waves. Annu. Rev. Fluid Mech. 38, 395425.CrossRefGoogle Scholar
Konyaev, K., Sabinin, K. & Serebryany, A. 1995 Large-amplitude internal waves at the Mascarene Ridge in the Indian Ocean. Deep-Sea Res. I 42, 20752081.CrossRefGoogle Scholar
Leblond, P. H. & Mysak, L. A. 1978 Waves in the Ocean. Elsevier.Google Scholar
Lighthill, J. 1978 Waves in Fluids. Cambridge University Press.Google Scholar
Marshall, J., Hill, C., Perelman, L. & Adcroft, A. 1997 Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling. J. Geophys. Res. 102, 57335752.Google Scholar
Mathur, M. & Peacock, T. 2009 Internal wave beam propagation in non-uniform stratifications. J. Fluid Mech. 639 (1), 133152.CrossRefGoogle Scholar
Maugé, R. & Gerkema, T. 2008 Generation of weakly nonlinear nonhydrostatic internal tides over large topography: a multi-modal approach. Nonlinear Process. Geophys. 15, 233244.Google Scholar
New, A. L. 1988 Internal tidal mixing in the Bay of Biscay. Deep-Sea Res. 35 (5), 691709.Google Scholar
New, A. L. & Pingree, R. D. 1990 Large-amplitude internal soliton packets in the central Bay of Biscay. Deep-Sea Res. 37 (3), 513524.CrossRefGoogle Scholar
New, A. L. & Pingree, R. D. 1992 Local generation of internal soliton packets in the central Bay of Biscay. Deep-Sea Res. 39 (9), 15211534.CrossRefGoogle Scholar
New, A. L. & da Silva, J. C. B. 2002 Remote-sensing evidence for the local generation of internal soliton packets in the central Bay of Biscay. Deep-Sea Res. I 49, 915934.CrossRefGoogle Scholar
Ostrovsky, L. A. & Stepanyants, Y. A. 1989 Do internal solitons exist in the ocean? Rev. Geophys. 27, 293310.CrossRefGoogle Scholar
Pingree, R. D. & New, A. L. 1991 Abyssal penetration and bottom reflection of internal tidal energy in the Bay of Biscay. J. Phys. Oceanogr. 21, 2839.Google Scholar
da Silva, J. C. B., New, A. L. & Azevedo, A. 2007 On the role of SAR for observing ‘local generation’ of internal solitary waves off the Iberian Peninsula. Can. J. Remote Sens. 33 (5), 388403.CrossRefGoogle Scholar
da Silva, J. C. B., New, A. L. M. & Magalhaes, J. M. 2009 Internal solitary waves in the Mozambique Channel: Observations and interpretation. J. Geophys. Res. 114, C05001.Google Scholar
Staquet, C., Sommeria, J., Goswami, K. & Mehdizadeh, M. 2006 Propagation of the Internal Tide from a Continental Shelf: Laboratory and Numerical Experiments. In Sixth International Symposium on Stratified Flows, Perth, Australia, pp. 539–544.Google Scholar
Thomas, N. H. & Stevenson, T. N. 1972 A similarity solution for viscous internal waves. J. Fluid Mech. 54, 495506.Google Scholar
Thorpe, S. A. 1987 Reflection of internal waves from a uniform slope. J. Fluid Mech. 178, 279302.CrossRefGoogle Scholar
Thorpe, S. A. 1998 Nonlinear reflection of internal waves at a density discontinuity at the base of the mixed layer. J. Phys. Oceanogr. 28, 18531860.Google Scholar
Zhang, H. P., King, B. & Swinney, H. L. 2007 Experimental study of internal gravity waves generated by supercritical topography. Phys. Fluids 19 (9), 096602.CrossRefGoogle Scholar
Zhang, K. Q. & Marotzke, J. 1999 The importance of open-boundary estimation for an Indian Ocean GCM-data synthesis. J. Mar. Res. 57 (2), 305334.CrossRefGoogle Scholar