Journal of Fluid Mechanics

Rapid distortion analysis and direct simulation of compressible homogeneous turbulence at finite Mach number

C.  Cambon a1, G. N.  Coleman a2 and N. N.  Mansour a3
a1 Laboratoire de Mécanique des Fluides et d'Acoustique, URA CNRS no. 263, Ecole Centrale de Lyon, 69130 Ecully, France
a2 Center for Turbulence Research, Stanford University, Stanford, CA 94305-3030, USA
a3 NASA Ames Research Center, Moffett Field, CA 94035-1000, USA

Article author query
cambon c   [Google Scholar] 
coleman gn   [Google Scholar] 
mansour nn   [Google Scholar] 


The effect of rapid mean compression on compressible turbulence at a range of turbulent Mach numbers is investigated. Rapid distortion theory (RDT) and direct numerical simulation results for the case of axial (one-dimensional) compression are used to illustrate the existence of two distinct rapid compression regimes. These regimes – the nearly solenoidal and the ‘pressure-released’ – are defined by a single parameter involving the timescales of the mean distortion, the turbulence, and the speed of sound. A general RDT formulation is developed and is proposed as a means of improving turbulence models for compressible flows. In contrast to the well-documented observation that ‘compressibility’ (measured, for example, by the turbulent Mach number) is often associated with a decrease in the growth rate of turbulent kinetic energy, we find that under rapid distortion compressibility can produce an amplification of the kinetic energy growth rate. We also find that as the compressibility increases, the magnitude of the pressure–dilation correlation increases, in absolute terms, but its relative importance decreases compared to the magnitude of the kinetic energy production.

(Published Online April 26 2006)
(Received December 8 1992)
(Revised May 7 1993)