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On wave-action and its relatives

Published online by Cambridge University Press:  19 April 2006

D. G. Andrews  and
M. E. Mcintyre
D. G. Andrews
Affiliation:
U.K. Universities’ Atmospheric Modelling Group, Reading, Berkshire, England Present address: Meteorology Department, Massachusetts Institute of Technology, Cambridge.
M. E. Mcintyre
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

Conservable quantities measuring ‘wave activity’ are discussed. The equation for the most fundamental such quantity, wave-action, is derived in a simple but very general form which does not depend on the approximations of slow amplitude modulation, linearization, or conservative motion. The derivation is elementary, in the sense that a variational formulation of the equations of fluid motion is not used. The result depends, however, on a description of the disturbance in terms of particle displacements rather than velocities. A corollary is an elementary but general derivation of the approximate form of the wave-action equation found by Bretherton & Garrett (1968) for slowlyvarying, linear waves.

The sense in which the general wave-action equation follows from the classical ‘energy-momentum-tensor’ formalism is discussed, bringing in the concepts of pseudomomentum and pseudoenergy, which in turn are related to special cases such as Blokhintsev's conservation law in acoustics. Wave-action, pseudomomentum and pseudoenergy are the appropriate conservable measures of wave activity when ‘waves’ are defined respectively as departures from ensemble-, space- and time-averaged flows.

The relationship between the wave drag on a moving boundary and the fluxes of momentum and pseudomomentum is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 89 , Issue 4 , 27 December 1978 , pp. 647 - 664
Copyright
© 1978 Cambridge University Press

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