Energy Transfer and Spectra in Simulations of Two-dimensional
  Compressible Turbulence
  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 $M\approx0.34$
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.
