Parametric resonant triad interactions in a free shear layer
Abstract
We investigate the weakly nonlinear evolution of a triad of nearlyneutral modes superimposed on a mixing layer with velocity profile u bar equals Um + tanh y. The perturbation consists of a plane wave and a pair of oblique waves each inclined at approximately 60 degrees 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.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 October 1993
 Bibcode:
 1993STIN...9415751M
 Keywords:

 Flow Distribution;
 Flow Velocity;
 Free Flow;
 Interactional Aerodynamics;
 Mixing Layers (Fluids);
 Plane Waves;
 Shear Flow;
 Shear Layers;
 Velocity Distribution;
 Vortices;
 Amplification;
 Differential Equations;
 Integral Equations;
 Nonlinearity;
 Perturbation;
 Time Dependence;
 Fluid Mechanics and Heat Transfer