An exact theory of nonlinear waves on a Lagrangian-mean flow
Abstract
An exact generalized theory of Lagrangian-mean 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 Lagrangian-mean velocity and to finite-amplitude versions of the basic theorems on mean-flow 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:
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Journal of Fluid Mechanics
- Pub Date:
- December 1978
- DOI:
- Bibcode:
- 1978JFM....89..609A
- Keywords:
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- Euler-Lagrange 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