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 nearlyneutral modes superimposed on a mixing
layer with velocity profile u = u_{m} + 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
integrodifferential equation. The longtime 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.
(Subscribers Only)
