An exact theory of nonlinear waves on a Lagrangianmean flow
Abstract
An exact generalized theory of Lagrangianmean flow is constructed for describing the effect of oscillatory disturbances on the mean state. It is shown that there is a natural choice among the family of transformations considered by Eckart (1963) which leads to a simple yet exact definition of the generalized Lagrangianmean velocity and to finiteamplitude versions of the basic theorems on meanflow evolution. The approach leads to what may be the first exact definition of pseudomomentum, or wave 'momentum'. It is shown that the difference between the Lagrangian mean velocity and the pseudomomentum per unit mass is exactly irrotational whenever the total motion is irrotational. An application of this to inviscid acoustic streaming is given.
 Publication:

Journal of Fluid Mechanics
 Pub Date:
 December 1978
 DOI:
 10.1017/S0022112078002773
 Bibcode:
 1978JFM....89..609A
 Keywords:

 EulerLagrange Equation;
 Flow Theory;
 Nonlinear Systems;
 Oscillating Flow;
 Wave Interaction;
 Acoustic Streaming;
 Boussinesq Approximation;
 Flow Equations;
 Incompressible Flow;
 Mean;
 Momentum Transfer;
 Potential Flow;
 Rossby Regimes;
 Wave Dispersion;
 Wave Drag;
 Fluid Mechanics and Heat Transfer