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Initial and boundary value problems of internal gravity waves

Published online by Cambridge University Press:  26 April 2006

Sergey T. Simakov
Sergey T. Simakov
Affiliation:
Department of Mathematics, Physical Faculty, Moscow State University, Moscow 119899, Russia
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Abstract

The paper considers the generation of Boussinesq internal waves in the framework of the Green's function method. For certain domains it is shown how to construct Green's functions using the fundamental solution of the equation. The behaviour of the solution at large times for an impulsively started monochromatic point source is studied, attention being focused on the growth rate of the oscillation amplitude on the characteristic surfaces of the steady-oscillation equation which are emitted from the point source. In addition a simple extended source is considered, for which a focusing singularity phenomenon is shown to take place.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 248 , March 1993 , pp. 55 - 65
Copyright
© 1993 Cambridge University Press

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References

Anyutin, A. P. & Borovikov, V. A. 1986 Evolution of localized disturbances of a stratified fluid with variable Brunt–Vaisala frequency. Prikl. Mat. Mekh. 50, 670– 674.Google Scholar
Appleby, J. C. & Crighton, D. G. 1987 Internal gravity waves generated by oscillations of a sphere. J. Fluid Mech. 183, 439– 450.Google Scholar
Baines, P. G. 1967 Forced oscillations of an enclosed rotating fluid. J. Fluid Mech. 30, 533– 546.Google Scholar
Borovikov, V. A. 1988 The field of the point source of internal waves in a half-space with a variable Brunt–Vaisala frequency. Prikl. Mat. Mekh. 52, 536– 540.Google Scholar
Borovikov, V. A. 1990 The t → ∞ asymptotic behaviour of the Green's function of the equation of internal waves. Dokl. Akad. Nauk SSSR 313, 313– 316. (English transl. Sov. Phys. Dokl. 35, 631–633.)Google Scholar
Brekhovskikh, L. & Goncharov, V. 1985 Mechanics of Continua and Wave Dynamics. Springer. (Translation from Russian).
Devanathan, R. & Ramachadra Rao, A. 1973 Forced oscillations of a contained rotating stratified fluid. Z. Angew. Math. Mech. 53, 617– 623.Google Scholar
Dickinson, R. E. 1969 Propagators of atmospheric motions. 1. Excitation by point impulses. Rev. Geophys. 7, 483– 514.Google Scholar
Gabov, S. A. & Sveshnikov, A. G. 1986 Problems of Dynamics of Stratified Fluids. Moscow: Nauka (in Russian).
Gill, A. E. 1982 Atmosphere–Ocean Dynamics. Academic.
Gordon, D., Klement, U. R. & Stevenson, T. N. 1975 A viscous internal wave in a stratified fluid whose buoyancy frequency varies with altitude. J. Fluid Mech. 69, 615– 624.Google Scholar
Hadamard, J. 1932 Le Probléme de Cauchy et les Equations aux Dérivées Partielles Linéaires Hyperboliques. Paris: Hermann et Cie.
Hendershott, M. C. 1969 Impulsively started oscillations in a rotating stratified fluid. J. Fluid Mech. 36, 513– 527.Google Scholar
Larsen, H. 1969 Internal waves incident upon a knife edge barrier. Deep Sea Res. 16, 411– 419.Google Scholar
Lighthill, M. J. 1978 Waves in Fluids. Cambridge University Press.
Liu, R., Nicolau, D. & Stevenson, T. N. 1990 Waves from an oscillatory disturbance in a stratified shear flow. J. Fluid Mech. 219, 609– 619.Google Scholar
Miropol'skii, Yu. Z. 1981 Dynamics of Internal Gravity Waves in the Ocean. Leningrad: Gidrometeoizdat (in Russian.)
Mowbray, D. E. & Rarity, B. S. H. 1967 A theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density stratified liquid. J. Fluid Mech. 28, 1– 16.Google Scholar
Sekerzh-Zenkovich, S. Ya. 1979 A fundamental solution of the internal-wave operator. Dokl. Akad. Nauk SSSR 246, 286– 288. (English transl. Sov. Phys. Dokl. 24, 347-348.)Google Scholar
Voisin, B. 1991 Internal wave generation in uniformly stratified fluids. Part 1. Green's function and point sources. J. Fluid Mech. 231, 439–480.Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. John Wiley.
Wood, W. W. 1965 Properties of inviscid, recirculating flows. J. Fluid Mech. 22, 337– 346.Google Scholar
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