Nonlinearized Fourier Approach, Gasdynamic Coherence, and Shock-Turbulence Interaction

Abstract

The present paper considers, in a linearized context, the interaction between two gasdynamic objects: a turbulence model and, respectively, a planar shock discontinuity. The incident turbulence, regarded as a perturbation, is modelled by a nonstatistical/noncorrelative superposition of some finite (or point core) planar vortices. $\bullet$ The linearized (with shock) context assumes a minimal nonlinearity. It considers a linearized problem: a linear problem with a nonlinear subconscious (in the sense of P.D. Lax and A. Majda; see $\S$2). The resultant perturbation is regarded as a solution (``interaction solution") of such a linearized problem. $\bullet$ In presence of a nonlinear subconscious the interaction solution is essentially constructed as an admissible solution.