The study of the phenomenon of compressibility for modeling to second order has been made by several authors, and they concluded that models of the pressure-strain are not able to predict the structural evolution of the Reynolds stress. In particular studies and Simone Sarkar et al., a wide range of initial values of the parameters of the problem are covered. The observation of Sarkar was confirmed by the study of Simone et al. (1997,“The Effect of Compressibility on Turbulent Shear Flow: A Rapid Distortion Theory and Direct Numerical Simulation Study,” J. Fluid Mech., 330, p. 307;“Etude Théorique et Simulation Numérique de la Turbulence Compressible en Présence de Cisaillement où de Variation de Volume à Grande Échelle” thése, École Centrale de Lyon, France). We will then use the data provided by the direct simulations of Simone to discuss the implications for modeling to second order. The performance of different variants of the modeling results will be compared with DNS results.

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