Tollmien-Shlichting and sound waves interaction: general description and   nonlinear resonances
  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 relation equations, extracted from the linearization of the general system over boundary layer flow. Each such connection defines 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 vortical 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. Subjectclass: Primary 35Q30 ; Secondary 76F70, 35Q72; Keywords: keywords fluid mechanics, boundary layer, projector to eigen modes, Tollmien-Schlichting waves, acoustic waves, nonlinear resonance, N-wave system. 
A. Perelomova, S.Leble