SHOCK LAYERS FOR TURBULENCE MODELS

Abstract

The present work is devoted to an extension of the Navier–Stokes equations where the fluid is governed by two independent pressure laws. Several turbulence models typically enter this framework. The striking novelty over the usual Navier–Stokes equations stems from the impossibility to recast equivalently the system of interest in full conservation form. Opposing to systems of conservation laws, where the end states of the viscous shock are completely characterized by jump relations, the lack of conservation implies the absence of jump relations. We analyze the traveling wave behaviors according to the ratio of viscosities, and we show that the traveling wave solutions of our system tend to the traveling wave solutions of a fully conservative system. This result is used to exhibit asymptotic expansions of the end states. Such an asymptotic behavior achieves a deep physical interpretation when illustrated in the case of compressible turbulent flows.