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The interaction trapping of internal gravity waves

Published online by Cambridge University Press:  28 March 2006

O. M. Phillips
O. M. Phillips
Affiliation:
Mechanics Department, The Johns Hopkins University
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Abstract

It is shown that as a result of their non-linear interactions, internal gravity waves in an unbounded fluid can be trapped to a layer of finite depth by periodic small variations in either the density gradient or in a weak horizontal steady current. This trapping occurs when the vertical component of the wave-number is half that of the density gradient or of the current variations. The energy density of the wave motion trapped near the ocean surface decreases exponentially with depth over a distance that is inversely proportional to the magnitude of the variations in density gradient or in horizontal current speed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 34 , Issue 2 , 12 November 1968 , pp. 407 - 416
Copyright
© 1968 Cambridge University Press

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References

Benjamin, T. BROOKE 1968 Comments on Dr Phillips' paper. Sixth Symp. Naval Hydro. (1966) Washington D.C.: U.S. Office of Naval Research.
Hasselmann, K. 1967 A criterion for second-order nonlinear wave stability J. Fluid Mech. 30, 737–40.Google Scholar
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Phillips, O. M. 1968 On internal wave interactions. Sixth Symp. Naval Hydro. (1966) Washington D.C.: U.S. Office of Naval Research.