Forcing for statistically stationary compressible isotropic turbulence.

Linear forcing has been proposed as a useful method for forced isotropic turbulence simulations because it is a physically realistic forcing method with a straightforward implementation in physical-space numerical codes [T. S. Lundgren, 'Linearly forced isotropic turbulence,' Annual Research Briefs (Center for Turbulence Research, Stanford, CA, 2003), p. 461; C. Rosales and C. Meneveau, 'Linear forcing in numerical simulations of isotropic turbulence: Physical space implementations and convergence properties,' Phys. Fluids 17, 095106 (2005)]. Here, extensions to the compressible case are discussed. It is shown that, unlike the incompressible case, separate solenoidal and dilatational parts for the forcing term are necessary for controlling the stationary state of the compressible case. In addition, the forcing coefficients can be cast in a form that allows the control of the stationary state values of the total dissipation (and thus the Kolmogorov microscale) and the ratio of dilatational to solenoidal dissipation. Linear full spectrum forcing is also compared to its low wavenumber restriction. Low wavenumber forcing achieves much larger Taylor Reynolds number at the same resolution. Thus, high Reynolds number asymptotics can be more readily probed with low wavenumber forced simulations. Since, in both cases, a solenoidal/dilatational decomposition of the velocity field is required, the simplicity of the full spectrum linear forcing implementation in physical-space numerical codes is lost. Nevertheless, low wavenumber forcing can be implemented without using a full Fourier transform, and so is computationally less demanding. [ABSTRACT FROM AUTHOR]