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On the generation and evolution of internal gravity waves

Published online by Cambridge University Press:  20 April 2006

Faiza S. Lansing  and
Tony Maxworthy
Faiza S. Lansing
Affiliation:
Departments of Mechanical and Aerospace Engineering, University of Southern California, Los Angeles, California 90089-1453 Present address: Tracking Systems and Applications Section, Jet Propulsion Laboratory, Pasadena, California 91109.
Tony Maxworthy
Affiliation:
Departments of Mechanical and Aerospace Engineering, University of Southern California, Los Angeles, California 90089-1453
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Abstract

In order to study the tidal generation and evolution of internal waves, both experimentally and theoretically, a two-dimensional two-layer model has been developed. The laboratory model consists of two immiscible fluid layers in a long wave tank, where time-dependent flow can be created by towing a suitably shaped obstacle with a sinusoidal motion. The effects of changing the Froude number and the ratio of the depths of the two fluid layers on the shape of the interface are studied. The first theoretical model considers the motion to be quasi-steady, allowing only a balance between buoyancy and inertial forces, and is in reasonable agreement with the experimental results for very slow motions and the initial phase of the tidal cycle only. A more complete numerical solution is based on the vortex-point method in which the interface is modelled by a set of discrete vortices, while the rigid boundaries, which include the obstacle, are modelled by a source distribution. The resulting governing equations are expressed in Lagrangian form, and the baroclinic generation of vorticity is related to the generation of source density, through two simultaneous integrodifferential equations. For small Froude numbers, the experimental and numerical results are in good quantitative agreement. At large Froude numbers, the numerical solution, which does not consider mixing between the two layers nor boundary-layer separation from the obstacle, gives a slight difference in the position of the maximum interface displacement from that found in the experiment.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 145 , August 1984 , pp. 127 - 149
Copyright
© 1984 Cambridge University Press

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References

Apel, J. R. & Holbrook, J. R. 1980 The Sulu Sea internal soliton experiment. Part A. Background and overview. EOS 61, 1009.Google Scholar
Baker, G. R., Merion, D. I. & Orszag, S. A. 1980 Vortex simulation of the Rayleigh-Taylor instability. Phys. Fluids 25, 1485.Google Scholar
Chereskin, T. K. 1983 Generation of internal waves in Massachusetts Bay. J. Geophys. Res. 88, 2649.Google Scholar
Farmer, D. M. & Smith, J. D. 1980 Tidal interaction of stratified flow with a sill in Knight Inlet. Deep-Dea Res. 27A, 239.Google Scholar
Gargett, A. E. 1976 Generation of internal waves in the Strait of Georgia, British Columbia. Deep-Sea Res. 23, 17.Google Scholar
Halpern, D. 1971 Observation on short period internal waves in Massachusetts Bay. J. Mar. Res. 29, 116.Google Scholar
Holbrook, J. R. & Apel, J. R. 1980 The Sulu Sea internal solitons. Part B. Observation of large-amplitude nonlinear internal waves. EOS 61, 1009.Google Scholar
Jaswon, M. A. & Symm, G. T. Integral Equation Methods in Potential Theory and Elastostatics. Academic.
Lansing, F. S. 1981 On the generation and evolution of interfacial waves. Ph.D. thesis, University of Southern California.
Lee, C. Y. & Beardsley, R. C. 1974 The generation of long internal waves in a weakly stratified shear flow. J. Geophys. Res. 79, 453–462.Google Scholar
Liu, A. K. 1981 Internal solitons in the Sulu Sea: comparison of wave theory with field data Dynatech Rep. DT-8204-01.Google Scholar
Long, R. R. 1954 Some aspects of the flow of stratified fluids. II. Experiments with a two-fluid system. Tellus 6, 97.Google Scholar
Longuet-Higgins, M. S. & Cokelet, E. D. 1978 The deformation of steep surface waves on water. II. Growth of normal mode instabilities. Proc. R. Soc. Lond. A 364.Google Scholar
Maxworthy, T. 1979 A note on the internal solitary waves produced by tidal flow over a three dimensional ridge. J. Geophys. Res. 84, 338.Google Scholar
Osborne, A. R. & Burch, T. 1980 Internal soliton in the Andaman Sea. Science 208, 451.Google Scholar
Rosenhead, L. 1931 The formation of vortices from surface discontinuity. Proc. R. Soc. Lond. A 134, 170.Google Scholar
Smith, J. D. & Farmer, D. M. 1977 Nonlinear internal waves and internal hydraulic jump in a fjord. In Geofluiddynamical Wave Mathematics, p. 42. University of Washington, Seattle.
Zarodny, S. J. & Greenberg, M. D. 1973 On a vortex sheet approach to the numerical calculation of water waves. J. Comp. Phys. 11, 440.Google Scholar