Journal of Fluid Mechanics

Compressible mixing layer growth rate and turbulence characteristics

A. W.  Vreman a1, N. D.  Sandham a2 and K. H.  Luo a2
a1 Department of Applied Mathematics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
a2 Department of Aeronautical Engineering, Queen Mary and Westfield College, Mile End Road, London E1 4NS, UK

Article author query
vreman aw   [Google Scholar] 
sandham nd   [Google Scholar] 
luo kh   [Google Scholar] 


Direct numerical simulation databases have been used to study the effect of compressibility on mixing layers. The simulations cover convective Mach numbers from 0.2 to 1.2 and all contain a fully resolved turbulent energy cascade to small spatial scales. Statistical information is extracted from the databases to determine reasons for the reduced growth rate that is observed as the convective Mach number is increased. It is found that the dilatational contribution to dissipation is negligible even when eddy shocklets are observed in the flow. Also pressure-dilatation is not found to be significant. Using an accurate relation between the momentum thickness growth rate and the production of turbulence kinetic energy together with integrated equations for the Reynolds stress tensor it is shown that reduced pressure fluctuations are responsible for the changes in growth rate via the pressure–strain term. A deterministic model for the required pressure fluctuations is given based on the structure of variable-density vortices and the assumption that the limiting eddies are sonic. Simple anisotropy considerations are used to close the averaged equations. Good agreement with turbulence statistics obtained from the simulations is found.

(Published Online April 26 2006)
(Received June 7 1995)
(Revised March 11 1996)