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Internal waves in a continuously stratified atmosphere or ocean

Published online by Cambridge University Press:  28 March 2006

John W. Miles
John W. Miles
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, La Jolla, California
Also Department of the Aerospace and Mechanical Engineering Sciences.
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Abstract

A stably stratified shear flow has the velocity profile V(1 - e−y/h) and the density profile log(ρ/ρ) = σ(1 − e−y/h) in 0 < y < ∞ and is bounded by the rigid plane y = 0. It is proved that small disturbances with respect to this basic flow are stable for all wavelengths and Richardson numbers. The eigenvalues for neutral disturbances (internal gravity waves) are enumerated. The results are applicable to the atmosphere and to an infinitely deep ocean.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 28 , Issue 2 , 8 May 1967 , pp. 305 - 310
Copyright
© 1967 Cambridge University Press

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References

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Eliassen, A., Høiland, E. & Riis, E. 1953 Two-Dimensional Perturbation of a Flow with Constant Shear of a Stratified Fluid. Institute for Weather and Climate Research, Norwegian Academy of Sciences and Letters, Publ. no. 1.
Hughes, T. H. & Reid, W. H. 1965 J. Fluid Mech. 23, 715–35.
Miles, J. W. 1961 J. Fluid Mech. 10, 496–508.
Miles, J. W. 1963 J. Fluid Mech. 16, 209–27.
Taylor, G. I. 1931 Proc. Roy. Soc. A 132, 499–523; see also Taylor (1960).
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