NON-LINEAR WAVE PACKETS IN THE KELVIN-HELMHOLTZ INSTABILITY

The instability of two layers of immiscible inviscid and incompressible fluids in relative motion is studied with allowance for small, but finite, disturbances and for spatial as well as temporal development. By using the method of multiple scalng, a generalized formulation of the amplitude equation is obtained, applicable to both stable and marginally unstable regions of parameter space. Of principal concern is the neighbourhood of the critical point for instability, where weakly nonlinar solutions can be found for arbitrary initial conditions. Numerical solutions of the amplitude equation (a nonlinear, unstable Klein-Gordon equation ) are presented for the case of nonlinear stabilization.