10.1 Effects of Compressibility in Free-Shear Flows. Observations

To understand and model compressibility-induced effects on turbulence is an important topic, as these effects are significant in many engineering applications, particularly in the fields of propulsion and supersonic aerodynamics, which are concerned with jets or wakes subjected to large velocity and density gradients. The compressible plane mixing layer is a generic problem for these applications, and explaining and modeling how compressibility reduces turbulent mixing in a shear layer has motivated the large research effort devoted to this topic during the 1980s and 1990s. Mixing usually refers to interpenetration of two streams. It is characterized by two scales: a length scale ? and a velocity scale ? U, which evaluate the thickness of the interface and intensity of the fluctuations, respectively. The reduction of mixing by compressibility is illustrated in Fig. 10.1 in which is the previously mentioned thickness and M _c = ? U/a is the convective Mach number, with a the average speed of sound.

Figure 10.1: Dependence of shear-layer growth rate on convective Mach number. DNS and experimental results from Pantano and Sarkar (2002).

There is now a consensus in the literature that the intrinsic compressibility (nonzero-velocity divergence in Mach-number-dependent flows) of a turbulent velocity field tends to reduce the amplification rate of turbulent kinetic energy produced by mean-velocity gradients, with respect to the solenoidal case. These effects were particularly investigated in shear flows, including both experimental and numerical studies of the plane...