On the Excitation of Instability Waves in Plane Poisuille Flow by a Concentrated Source at the Wall

Abstract

The paper addresses the excitation of instability waves in plane Poiseuille flow by means of a concentrated source at the wall. The aim of this paper is to investigate the relation between the source amplitude and the excited wave amplitude for  various flow and source parameters .The source is modeled by a time harmonic Dnae function and the generated disturbance is investigated By applying Founrier transform on the resulting linearized Navier-Stokes equation in the streamwise direction, the problem is resolved using inverse Fourier transform and the residue theorem. The theoretical formulation explains some observations by previous experiments on similar cases of excitation. Moreover, the calculations demonstrate that the disturbance amplitude increases as the excitation frequency decreases for a fixed Reynolds number, while, on the other hand, it  increases as Reynolds number decreases for a fixed frequency.