A Contribution to the Analysis of Reynolds Stress Models for Shock Turbulence Interaction
This work in mechanics deals with compressible anisotropic turbulence interacting with a shock wave for Reynolds Stress Models. Physically, the turbulent mass flux should be taken into account because of the Favre average linked to the compressible behaviour of the flow. However, this term is mostly neglected. The main results of this work state that a shock wave interacting with turbulence may become strongly unstable as soon as this term is not considered or poorly modelled. To ensure structural and then multidimensional stability of the shock, we prove that it is necessary to define a related time scale with sufficiently high magnitude and correctly defined magnitude variations. The turbulent mass flux is defined thanks to Ristorcelli modelling, until now the only one to be realisable, objective and with entropic characterization. With these properties, we use the recent concept of kinetic relations to define shock solutions in a non conservative framework. With this concept, we show how to generalize the Majda and the Lopatinski conditions to study one-dimensional and multidimensional stability of shock solutions in a non conservative framework.