Solenoidal linear forcing for compressible, statistically steady, homogeneous isotropic turbulence with reduced turbulent Mach number oscillation

This study investigates a solenoidal linear forcing scheme with reduced oscillation of a turbulent Mach number MT for direct numerical simulations (DNS) of statistically steady, homogeneous isotropic turbulence. A conventional linear forcing scheme results in a large temporal oscillation of MT, where the maximum MT reaches about 1.1 times the time-averaged MT. Therefore, strong shocklets are generated when MT becomes large although such strong shocklets hardly appear when MT is close to the time-averaged value. DNS with the proposed forcing scheme confirms that the temporal oscillation of MT is effectively reduced by adjusting a forcing coefficient with a ratio between velocity variance and its steady state value prescribed as a parameter. The time-dependent forcing coefficient results in the variation of the power input to kinetic energy. Therefore, the temporal oscillation of the Reynolds number for this forcing scheme is as large as that for the conventional linear forcing. The ratio between the solenoidal and dilatational kinetic energy dissipation rates increases with MT, and the MT dependence is consistent between the present solenoidal linear forcing and the low-wavenumber solenoidal forcing in wavenumber space. The skewness and flatness of the velocity derivative become large compared with incompressible turbulence when MT exceeds 0.6. Both average and root-mean-squared fluctuation of the shock Mach number of shocklets increase with MT. The most typical thickness of shocklets decreases with MT and asymptotically approaches about 1.5 times the Kolmogorov scale. The shocklet thickness normalized by the Kolmogorov scale hardly depends on the Reynolds number.