Rapid distortion analysis of compressible turbulence in ideal gas: Part 2 - Density averaged moments

We perform rapid distortion analysis of linearized, inviscid Favre-averaged Navier Stokes equation. This study - Favre-averaged Rapid Distortion Theory (F-RDT)- investigates the evolution of density weighted fluctuating moments. The fluid is assumed to be an ideal gas. The F-RDT formulation comprises of a closed set of 65 ordinary differential equations for the case of homogenous mean shear field. With $S \mathord{\left/ {\vphantom {S {R\widetilde{T}}}} \right. \kern-\nulldelimiterspace} {R\widetilde{T}}$ as compressibility parameter ($S=$magnitude of mean shear, $R=$gas constant, $\widetilde{\mbox{T}}=$density weighted mean temperature), the versatility of the formulation is demonstrated by recovering both the incompressible and Burgers limit behaviors. Results for several intermediate cases-between the above two extreme limits-are also obtained. Favre-averaged Reynolds stresses, temperature variance, density variance and various cross-correlations will be discussed.