A study of initial conditions' effects on thermal properties of compressible homogeneous sheared non-isentropic turbulence using rapid distortion theory (RDT)

This paper investigates the effect of initial conditions characterized by compressibility of turbulence on the changes in scalar such as density, temperature, and pressure within the framework of rapid distortion theory (RDT) in the case of non-isentropic turbulence. This study is a follow-up of the basic work carried out by A. Simone, G.N. Coleman and C. Cambon [J. Fluid Mech. 330, 307 (1997)] in the case of quasi-isentropic turbulence and the previous work of M. Riahi and T. Lili [Fluid Dyn. Res. 52, 025501 (2020)] in the case of non-isentropic turbulence. RDT was used to examine the behavior of the root mean square (rms) fluctuations of density, temperature, and pressure. The coupling between these rms quantities, the partition factor, and the polytropic coefficient was also studied. RDT equations were solved numerically using a code that solves directly evolution equa-tions of two-point spectral correlations for compressible homogeneous sheared non-isentropic turbulence. The RDT analysis was carried out for various initial turbulent Mach numbers Mt0 ranging from 0.1 to 0.4, and the initial compressible turbulence is to be one of the three states concerning the fraction of kinetic energy x0: solenoidal (x0 = 0), mixed (x0 = 0.6), and dilata-tional (x0 = 1) (x0 is the ratio of the initial dilatational kinetic energy to the initial total kinetic energy). It is shown from this study that the changes in scalars are strongly dependent on the initial conditions. Magnitudes and asymptotic values of rms thermodynamics fluctuations and correlations between these thermodynamics fluctuations depend of Mt0. For large times, the isentropic state of the flow is well observed whatever Mt0 and x0.