Excitation of Direct Resonances in Plane Poiseuille Flow

Abstract

The direct resonance mechanism between vertical vorticity and vertical velocity is studied for plane Poiseuille flow. The resonance term, obtained from the initialvalue problem, has been determined numerically for various initial disturbances. The amplitude, in wave‐number space, is found to decay with time for all resonances. Because of its appearance in the Laplace‐transform plane as a double pole, it is shown that a resonance term will have an initial amplitude which grows with Reynolds number, thus indicating that resonances will dominate the initial development of a disturbance at large Reynolds number.