Growth and decay of perturbations at an interface in a stagnation counterflow

Abstract

Integral-transform theory is used to solve the problem of sinusoidal initial perturbations in a planar stagnation counterflow, with extension to the axisymmetric case. The two incompressible fluids are assumed to be inviscid, so that across the initially plane interface the velocity shear is a velocity slip which grows linearly with the distance from the stagnation point. The solution for the interface displacement shows a competition between an amplification produced by the shear instability and a decay produced by the stretching effect of the accelerating unperturbed flow. At early times the interface perturbation grows exponentially with time, but eventually the stretching process reduces the interface displacement to a magnitude comparable to the initial perturbation.