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A numerical simulation of Kelvin-Helmholtz waves of finite amplitude

Published online by Cambridge University Press:  29 March 2006

P. C. Patnaik
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado 80303 Present address: Science Applications Inc., 1205 Prospect Street, La Jolla, California 92037.
F. S. Sherman
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, California 94720
G. M. Corcos
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, California 94720

Abstract

A number of initial- and boundary-value problems for the Boussinesq equations are solved by a finite-difference technique, in an attempt to see how a stably-stratified horizontal shear layer rolls up into horizontally periodic billows of concentrated vorticity, such as are frequently observed in the atmosphere and oceans. This paper describes the methods, results and accuracy of the numerical simulations. The results are further analysed and approximately reproduced by a simple semi-analytic model in Corcos & Sherman (1976).

Type
Research Article
Copyright
© 1976 Cambridge University Press

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References

Amsden, A. A. & Harlow, F. H. 1964 Phys. Fluids, 7, 327.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Benney, D. J. & Bergeron, R. F. 1969 Stud. Appl. Math. 48, 181.
Browand, F. K. & Wang, Y. H. 1972 An experiment on the growth of small disturbances at the interface between two streams of different densities and velocities. Proc. Int. Symp. on Stratified Flows, Novosibirsk, USSR.
Browand, F. K. & Winant, C. D. 1973 Boundary-Layer Met. 5, 67.
Chorin, A. J. 1968 Math. Comp. 22, 745.
Chorin, A. J. 1969 Math. Comp. 23, 341.
Christiansen, J. P. 1973 J. Comp. Phys. 13, 363.
Corcos, G. M. & Sherman, F. S. 1976 J. Fluid Mech. 73, 241.
Delisi, D. P. & Corcos, G. M. 1973 Boundary-Layer Met. 5, 43.
Fasel, H. 1974 Untersuchungen zum Problem des Grenzschichtumschlages durch numerische Integration der Navier-Stokes Bleichungen. Dissertation, Institut A für Mechanik, University of Stuttgart.
Garrett, C. & Munk, W. 1972 Deep-Sea Res. 19, 823.
Maslowe, S. A. 1973 Boundary-Layer Met. 5, 43.
Maslowe, S. A. & Thomson, J. M. 1971 Phys. Fluids, 14, 453.
Maxworthy, T. & Browand, F. K. 1975 Experiments in rotating and stratified flows with oceanographic application Ann. Rev. Fluid Mech. 7, 273.Google Scholar
Michalke, A. 1965 J. Fluid Mech. 23, 521.
Patnaik, P. C. 1973 A numerical study of finite-amplitude Kelvin-Helmholtz waves. Ph.D. dissertation, Department of Mechanical Engineering, University of California, Berkeley.
Robinson, J. L. 1974 J. Fluid Mech. 63, 723.
Schade, H. 1964 Phys. Fluids, 7, 623.
Stuart, J. T. 1967 J. Fluid Mech. 29, 417.
Takata, H. 1975 J. Met. Soc. Japan, 53, 1.
Thorpe, S. A. 1971 J. Fluid Mech. 46, 299.
Thorpe, S. A. 1973 Boundary-Layer Met. 5, 95.
Winant, C. D. & Browand, F. K. 1974 J. Fluid Mech. 63, 237.
Woods, J. D. & Wiley, R. L. 1972 Deep-Sea Res. 19, 87.
Zabusky, N. J. & Deem, G. S. 1971 J. Fluid Mech. 47, 353.