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 M-T for direct numerical simulations (DNS) of statistically steady, homogeneous isotropic turbulence. A conventional linear forcing scheme results in a large temporal oscillation of M-T, where the maximum M-T reaches about 1.1 times the time-averaged M-T. Therefore, strong shocklets are generated when M-T becomes large although such strong shocklets hardly appear when M-T is close to the time-averaged value. DNS with the proposed forcing scheme confirms that the temporal oscillation of M-T 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 M-T, and the M-T 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 M-T exceeds 0.6. Both average and root-mean-squared fluctuation of the shock Mach number of shocklets increase with M-T. The most typical thickness of shocklets decreases with M-T and asymptotically approaches about 1.5 times the Kolmogorov scale. The shocklet thickness normalized by the Kolmogorov scale hardly depends on the Reynolds number.

Automated summary

This study investigates a solenoidal linear forcing scheme with reduced oscillation of a turbulent Mach number M-T for direct numerical simulations of homogeneous isotropic turbulence. Adjusting the forcing coefficient effectively reduces the temporal oscillation of M-T and increases the power input to kinetic energy. The solenoidal and dilatational kinetic energy dissipation rates increase with M-T, and the shocklet thickness normalized by the Kolmogorov scale hardly depends on the Reynolds number.