Three-wave nonlinear interactions of disturbances in supersonic boundary layer on the solid and porous surfaces

Abstract

The interaction of disturbances in supersonic boundary layer is considered within the framework of the weakly nonlinear stability theory for the Mach number M = 2 on the solid and porous surfaces. The interrelations in several triplets composed of two- and three-dimensional waves at the frequencies related by the phase synchronization conditions were modelled. It was found that their interactions on the solid surface are much stronger in the asymmetric triplet. It was found that on a porous surface, the linear increments of vortex disturbances increase considerably, the region of dangerous frequencies widens, and the spatial extension of the existence of growing oscillations increases. Nonlinear interactions are, as a rule, much more intense in comparison with the case of an solid surface; they realize in a broad frequency range, which results to a broadband growth of the Tollmien — Schlichting subharmonic vortex waves. An increase in the surface porosity leads to the intensification of nonlinear processes.