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Equilibrium states of homogeneous compressible turbulence subjected to rapid shear is studied using rapid distortion theory (RDT). The purpose of this study is to determine the numerical solutions of unsteady linearized equations governing double correlations spectra evolution. In this work, RDT code developed by authors solves these equations for compressible homogeneous shear flows. Numerical integration of these equations is carried out using a second-order simple and accurate scheme. The two Mach numbers relevant to homogeneous shear flow are the turbulentMach numberM t , given by the root mean square turbulentvelocityfluctuations divided by the speed of sound, and the gradient Mach numberM g which is the mean shear rate times the transverse integral scale of the turbulence divided by the speed of sound. Validation of this code is performed by comparing RDT results with direct numerical simulation (DNS) of [A. Simone, G.N. Coleman, and C. Cambon, Fluid Mech. 330, 307 (1997)] and [S. Sarkar, J. Fluid Mech. 282, 163 (1995)] for various values of initial gradient Mach numberM g 0. It was found that RDT is valid for small values of the non-dimensional times St (St < 3.5). It is important to note that RDT is also valid for large values of St (St > 10) in particular for large values of M g 0. This essential feature justifies the resort to RDT in order to determine equilibrium states in the compressible regime.


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