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A conservation law for internal gravity waves

Published online by Cambridge University Press:  11 April 2006

Michael Milder
Michael Milder
Affiliation:
Physical Dynamics Inc., P.O. Box 3800, Santa Monica, California 90403
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Abstract

The scaled vorticity Ω/N and strain ∇ ζ associated with internal waves in a weak density gradient of arbitrary depth dependence together comprise a quantity that is conserved in the usual linearized approximation. This quantity I is the volume integral of the dimensionless density DI = ½[Ω2/N2 + (∇ ζ)2]. For progressive waves the ‘kinetic’ and ‘potential’ parts are equal, and in the short-wavelength limit the density DI and flux FI are related by the ordinary group velocity: FI = DIcg. The properties of DI suggest that it may be a useful measure of local internal-wave saturation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 78 , Issue 2 , 23 November 1976 , pp. 209 - 216
Copyright
© 1976 Cambridge University Press

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References

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