A note on the wave action density of a viscous instability mode on a laminar freeshear flow
Abstract
Using the assumptions of an incompressible and viscous flow at large Reynolds number, we derive the evolution equation for the wave action density of an instability wave traveling on top of a laminar freeshear flow. The instability is considered to be viscous; the purpose of the present work is to include the cumulative effect of the (locally) small viscous correction to the wave, over length and time scales on which the underlying base flow appears inhomogeneous owing to its viscous diffusion. As such, we generalize our previous work for inviscid waves. This generalization appears as an additional (but usually nonnegligible) term in the equation for the wave action. The basic structure of the equation remains unaltered.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 November 1994
 Bibcode:
 1994STIN...9518212B
 Keywords:

 Base Flow;
 Computational Fluid Dynamics;
 Flow Stability;
 Incompressible Flow;
 Viscous Flow;
 Wave Interaction;
 Wave Propagation;
 Boundary Value Problems;
 Conservation Equations;
 High Reynolds Number;
 Mathematical Models;
 Fluid Mechanics and Heat Transfer