Journal of Fluid Mechanics

On wave-action and its relatives

D. G.  Andrews a1p1 and M. E.  Mcintyre a2
a1 U.K. Universities’ Atmospheric Modelling Group, Reading, Berkshire, England
a2 Department of Applied Mathematics and Theoretical Physics, University of Cambridge

Article author query
andrews dg   [Google Scholar] 
mcintyre me   [Google Scholar] 


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.

(Published Online April 19 2006)
(Received October 9 1976)
(Revised July 12 1978)

p1 Present address: Meteorology Department, Massachusetts Institute of Technology, Cambridge.