Volume 2, Number 1, Winter 1994
PARAMETRIC RESONANT TRIAD INTERACTIONS
IN A FREE SHEAR LAYER
R. MALLIER AND S.A. MASLOWE
Abstract. We investigate the weakly nonlinear evolution
of a triad of nearly-neutral modes superimposed on a mixing
layer with velocity profile u = um + tanhy. The perturbation
consists of a plane wave and a pair of oblique waves each
inclined at approximately 60° to the mean flow direction.
Because the evolution occurs on a relatively fast time scale,
the critical layer dynamics dominate the process and the
amplitude evolution of the oblique waves is governed by an
integro-differential equation. The long-time solution of this
equation predicts very rapid (exponential of an exponential)
amplification and we discuss the pertinence of this result to
vortex pairing phenomena in mixing layers.