Abstract

Tollmienn-Shlichting and Sound Waves Interaction: Nonlinear Resonances

S.Leble (Kaliningrad State University, Kaliningrad, Russia); A.Perelomova (Faculty of Applied Physics and Mathematics, The Technical University of Gdansk, Gdansk, Poland)

e-mail: leble@mif.pg.gda.pl

The general hydro-thermodynamic system of equations in 2+1 dimensions with arbitrary equations of state (Taylor series approximation) is split to eigen modes: Tollmienn-Schlichting (TS) wave and two acoustic ones. A mode definition is realized via local connection equations, extracted from the linearization of the general system over boundary layer flow. Each such connection define the subspace and the corresponding projector. So the division is performed locally and could help in initial (or boundary) problems formulation. The general nonlinearity account determines the specific form of interaction between acoustic and boundary layer perturbation fields. After the next projecting to a subspace of Orr-Sommerfeld equation solution for the TS wave and the corresponding procedure for acoustics, the equations go to one-dimensional system that describes evolution along the basic stream. A new mechanism of nonlinear resonance excitation of the TS wave by sound is proposed and modelled via four-wave interaction. The velocities and nonlinear constants of the four-wave system are evaluated via integrals of the Orr-Sommerfeld equation solutions and sound wave eigenfunctions.

Section : 7