Kinetic and internal energy transfer in implicit largeeddy simulations of forced compressible turbulence
Abstract
We revisit the problem of how energy transfer through the turbulent cascade operates in compressible hydrodynamic turbulence. In general, there is no conservative compressible cascade since the kinetic and internal energy reservoirs can exchange energy through pressure dilatation. Moreover, statistically stationary turbulence at high Mach number can only be maintained in nearly isothermal gas, i.e., if excess heat produced by shock compression and kinetic energy dissipation is continuously removed from the system. We mimic this process by a linear cooling term in numerical simulations of turbulence driven by stochastic forcing. This allows us to investigate turbulence statistics for a broad range of Mach numbers. We compute the rate of change of kinetic and internal energy in wavenumber shells caused by advective, compressive, and pressure dilatation effects and constrain powerlaw fits to compressible turbulence energy spectra to a range of wave numbers in which the total energy transfer is close to zero. The resulting scaling exponents are significantly affected by the forcing. Depending on the root mean square Mach number, we find a nearly constant advective component of the crossscale flux of kinetic energy at intermediate wave numbers for particular mixtures of solenoidal and compressive modes in the forcing. This suggests the existence of a natural, Mach number dependent mixture of forcing modes. Our findings also support an advectiondominated regime at high Mach numbers with specific scaling exponents (Burgers scaling for the pure velocity fluctuation u and Kolmogorov scaling for the massweighted variable v =ρ^{1 /3}u ).
 Publication:

Physical Review E
 Pub Date:
 October 2019
 DOI:
 10.1103/PhysRevE.100.043116
 arXiv:
 arXiv:1906.12228
 Bibcode:
 2019PhRvE.100d3116S
 Keywords:

 Physics  Fluid Dynamics;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 Astrophysics  Astrophysics of Galaxies
 EPrint:
 accepted for publication in Phys. Rev. E, 20 pages, 14 figures