The Stabilizing Effect of Compressibility in Turbulent Shear Flow

Direct numerical simulation of turbulent homogeneous shear ow is performed in order to clarify compressibility e ects on the turbulence growth in the ow. The two Mach numbers relevant to homogeneous shear ow are the turbulent Mach number Mt and the gradient Mach number Mg . Two series of simulations are performed where the initial values of Mg and Mt are increased separately. The growth rate of turbulent kinetic energy is observed to decrease in both series of simulations. This `stabilizing' e ect of compressibility on the turbulent energy growth rate is observed to be substantially larger in the DNS series where the initial value ofMg is changed. A systematic comparison of the di erent DNS cases shows that the compressibility e ect of reduced turbulent energy growth rate is primarily due to the reduced level of turbulence production and not due to explicit dilatational e ects. The reduced turbulence production is not a mean density e ect since the mean density remains constant in compressible homogeneous shear ow. The stabilizing e ect of compressibility on the turbulence growth is observed to increase with the gradient Mach number Mg in the homogeneous shear ow DNS. Estimates of Mg for the mixing layer and the boundary layer are obtained. These estimates show that the parameter Mg becomes much larger in the high-speed mixing layer relative to the highspeed boundary layer even though the mean ow Mach numbers are the same in the two ows. Therefore, the inhibition of turbulent energy production and consequent `stabilizing' e ect of compressibility on the turbulence (over and above that due to the mean density variation) is expected to be larger in the mixing layer relative to the boundary layer in agreement with experimental observations. 1Supported by National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681-0001.