Effect of shock waves on the statistics and scaling in compressible isotropic turbulence

The statistics and scaling of compressible isotropic turbulence in the presence of large-scale shock waves are investigated by using numerical simulations at turbulent Mach number M_{t} ranging from 0.30 to 0.65. The spectra of the compressible velocity component, density, pressure, and temperature exhibit a k^{-2} scaling at different turbulent Mach numbers. The scaling exponents for structure functions of the compressible velocity component and thermodynamic variables are close to 1 at high orders n≥3. The probability density functions of increments of the compressible velocity component and thermodynamic variables exhibit a power-law region with the exponent -2. Models for the conditional average of increments of the compressible velocity component and thermodynamic variables are developed based on the ideal shock relations and are verified by numerical simulations. The overall statistics of the compressible velocity component and thermodynamic variables are similar to one another at different turbulent Mach numbers. It is shown that the effect of shock waves on the compressible velocity spectrum and kinetic energy transfer is different from that of acoustic waves.