Evolution of axisymmetric weakly turbulent mixtures interacting with shock or rarefaction waves

This paper deals with the interaction of a shock or a rarefaction wave with a weakly turbulent mixture of perfect gases. Assuming weak density-velocity fluctuations, Kovasznay decomposition applies and linear theories can be used to predict the evolution of the joint spectrum of density and velocity during the interaction. In this work, the upstream spectrum is restricted to axisymmetric fields free of acoustic perturbations, in order to comply with shock tube experimental conditions. Besides, spectral anisotropy is limited to a first order spherical harmonic decomposition. With these assumptions, transfer matrices can be obtained which relate the Reynolds stresses, turbulent mass flux and density variance after interaction to their counterparts before interaction. Results are given for both shock waves and rarefaction or compression waves; they are intended to help improve one-point statistical turbulence models applied to shock tube experiments.