Finiteamplitude waves in inviscid shear flows
Abstract
This paper examines the existence and properties of steady finiteamplitude waves of catseye form superposed on a unidirectional inviscid, incompressible shear flow. The problem is formulated as the solution of nonlinear Poisson equations for the stream function with boundary conditions on the unknown edges of the catseyes. The dependence of vorticity on stream function is assumed outside the catseyes to be as in the undisturbed flow, and uniform unknown vorticity is assumed inside. It is argued on the basis of a finite difference discretization that the problem is determinate, and numerical solutions are obtained for CouettePoiseuille channel flow. These are compared with the predictions of a weakly nonlinear theory based on the approach of Benney and Bergeron (1969) and Davis (1969). The phase speed of the waves is found to be linear in the wave amplitude.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 August 1982
 DOI:
 10.1098/rspa.1982.0108
 Bibcode:
 1982RSPSA.382..389M
 Keywords:

 Channel Flow;
 Finite Difference Theory;
 Inviscid Flow;
 Shear Flow;
 Stream Functions (Fluids);
 Wave Propagation;
 Boundary Conditions;
 Boundary Value Problems;
 Computational Fluid Dynamics;
 Incompressible Fluids;
 Poisson Equation;
 Vorticity;
 Fluid Mechanics and Heat Transfer