Scaling exponents for structure functions of the velocity, density, and entropy are computed for driven supersonic flows for rms Mach numbers of order unity, with numerical simulations using the piecewise parabolic method algorithm on grids of up to ${512}^3$ points. The driving is made up of either one or three orthogonal shear waves. In all cases studied, the compressible component of the velocity in the statistically steady regime is weaker than its solenoidal counterpart by roughly a factor of 6. Exponents for the longitudinal component of the velocity are comparable to what is found in the incompressible case and appear insensitive to the presence of numerous shocks. Scaling exponents of the transverse components of the velocity are comparable to those for the longitudinal component. Density and entropy structure functions display strong departures from linear scaling. Finally, the scaling of structure functions of the energy transfer is also given and compared with the Kolmogorov refined similarity hypothesis.

• Received 7 March 2002

DOI:https://doi.org/10.1103/PhysRevE.66.026301