Parametric resonant triad interactions in a free shear layer
Abstract
We investigate the weakly nonlinear evolution of a triad of nearly-neutral 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 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.
- 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