Advection of mass fraction in forced, homogeneous, compressible turbulence

In nearly isothermal, compressible turbulence of a nondense gas the mass fraction of an embedded passive scalar satisfies the same formal conservation equation as a passive scalar in incompressible turbulence. Direct numerical simulation of this system shows that the compressible turbulence modes are less efficient than the incompressible in transporting scalar spectral content from large to small scales. It is argued that the cause of this outcome is the reduced size of the integral length scale of the compressible velocity components vis á vis that of the incompressible velocity components, and this also explains the experimentally observed ineffectiveness of the dilatational velocity modes in determining scalar flux in homogeneous, compressible turbulence with a uniform mean scalar gradient.