Three-wave non-linear interaction in a three-dimensional compressible boundary layer

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摘要：

A perturbation method for analysis of non-linear wave interaction in three-dimensional compressible boundary layer is developed. The method is based on a biorthogonal eigenfunction system for three-dimensional compressible boundary layers. It is assumed that characteristic space and time scales of the disturbances are much less than space and time scales of non-linear development and an averaging technique in intermediate scales may be applied. The method is a generalization of Zelman's results for two-dimensional incompressible boundary layer. As an example, a three-wave interaction is considered. A numerical example for so-called Tollmien — Schlichting wave interaction shows the possibility of amplification for rather broad packets without an exact resonance synchronizm for three-wave interaction.

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Theoretical or Mathematical/ boundary layers compressible flow eigenvalues and eigenfunctions laminar to turbulent transitions resonance/ three-wave non-linear interaction three-dimensional compressible boundary layer perturbation method biorthogonal eigenfunction system averaging technique intermediate scale two-dimensional incompressible boundary layer Zelman's generalization Tollmien-Schlichting wave interaction exact resonance synchronism/ A4725F Boundary layer and shear turbulence A4715C Laminar boundary layers A0210 Algebra, set theory, and graph theory A4715F Stability of laminar flows A4740 Compressible flows shock and detonation phenomena