Numerical study of a turbulent flow compressed by a weak shock wave

Modification of a two-dimensional isotropic turbulent flow by passage of a weak shock wave was numerically studied by the explicit spectral collocation method with the Fourier series in the ranges of M(t) = 0.14-0.21 and M(s) = 1.06-1.14. The density Turbulent kinetic energy increased by 10 to 19 % and density fluctuation increased by 14 to 50 % in proportion to the shock wave Mach number. The amplification of turbulent kinetic energy did not change by increase of the turbulent Mach number, while that of density fluctuation decreased from 1.35 to 1.15. The augmentation of turbulent kinetic energy appeared al moderate and high wave numbers of the energy spectra and resulted in a reduction of the integral scale by 3.3 to 5.4 %. Modification mechanisms of turbulent kinetic energy, density fluctuation and vorticity were verified by their transport equations. It was shown that the decreased amplification of the density fluctuation by the increased turbulent Mach number attributed to the unchanged production terms and the negative density-dilatation correlation behind the shock wave. The vorticity-dilatation term was responsible for more than 80% of the total vorticity production at the shock front.