Energy Transfer and Spectra in Simulations of Two-dimensional Compressible Turbulence

Abstract

We present results of high-resolution numerical simulations of compressible 2D turbulence forced at intermediate spatial scales with a solenoidal white-in-time external acceleration. A case with an isothermal equation of state, low energy injection rate, and turbulent Mach number $M\approx 0.34$ without energy condensate is studied in detail. Analysis of energy spectra and fluxes shows that the classical dual-cascade picture familiar from the incompressible case is substantially modified by compressibility effects. While the small-scale direct enstrophy cascade remains largely intact, a large-scale energy flux loop forms with the direct acoustic energy cascade compensating for the inverse transfer of solenoidal kinetic energy. At small scales, the direct enstrophy and acoustic energy cascades are fully decoupled at small Mach numbers and hence the corresponding spectral energy slopes comply with theoretical predictions, as expected. At large scales, dispersion of acoustic waves on vortices softens the dilatational velocity spectrum, while the pseudo-sound component of the potential energy associated with coherent vortices steepens the potential energy spectrum.

10 pages, 6 figures. To appear in: Turbulence in Complex Conditions, Proc. Euromech/Ercoftac Colloquium 589, ed. M. Gorokhovski, Springer, 2018

References in corpus (8)

• Theory of Star Formation
• The Statistics of Supersonic Isothermal Turbulence
• HI power spectrum of the spiral galaxy NGC628
• Split energy cascade in turbulent thin fluid layers
• Energy transfer in compressible magnetohydrodynamic turbulence for isothermal self-gravitating fluids
• Probing interstellar turbulence in spiral galaxies using HI power spectrum analysis
• Exact relations for energy transfer in self-gravitating isothermal turbulence
• How vortices and shocks provide for a flux loop in two-dimensional compressible turbulence