Advection by polytropic compressible turbulence

Direct numerical simulation (DNS) is used to examine scalar correlation in low Mach number, polytropic, homogeneous, two-dimensional turbulence (M _s≤0.7) for which the initial conditions, Reynolds, and Mach numbers have been chosen to produce three types of flow suggested by theory: (a) nearly incompressible flow dominated by vorticity, (b) nearly pure acoustic turbulence dominated by compression, and (c) nearly statistical equipartition of vorticity and compressions. Turbulent flows typical of each of these cases have been generated and a passive scalar field imbedded in them. The results show that a finite-difference based computer program is capable of producing results that are in reasonable agreement with pseudospectral calculations. Scalar correlations have been calculated from the DNS results and the relative magnitudes of terms in low-order scalar moment equations determined. It is shown that the scalar equation terms with explicit compressibility are negligible on a long time-averaged basis. A physical-space EDQNM model has been adapted to provide another estimate of scalar correlation evolution in these same two-dimensional, compressible cases. The use of the solenoidal component of turbulence energy, rather than total turbulence energy, in the EDQNM model gives results closer to those from DNS in all cases.