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

Commun. Math. Anal.
Volume 8, Number 3 (2010), 66 - 91

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

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Abstract

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