ICASE Report No . 90-15 181997 ICASE THE ANALYSIS AND SIMULATION OF COMPRESSIBLE TURBULENCE

This paper considers compressible turbulent flows at low turbulent Mach numbers. Contrary to the general belief that such flows are almost incompressible , (i.e. the divergence of the velocity field remains small for all times), it is shown that even if the divergence of the initial velocity field is negligibly small, it can grow rapidly on a non-dimensional time scale which is the inverse of the fluctuating Mach number. An asymptotic theory which enables one to obtain a description of the flow in terms of its divergence-free and vorticity-free components has been developed to solve the initial-value problem. As a result, the various types of low Mach number turbulent regimes have been classified with respect to the initial conditions. Formulae are derived that accurately predict the level of compressibility after the initial transients have disappeared. These results are verified by extensive direct numerical simulations of isotropic turbulence. XResearch was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-18605 while all of the authors were in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23665.