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

TL;DR

This study uses high-resolution simulations to explore how compressibility alters the classical dual-cascade energy transfer in 2D turbulence, revealing new energy flux loops and spectral behaviors.

Contribution

It provides detailed analysis of energy spectra and fluxes in compressible 2D turbulence, highlighting modifications to the dual-cascade picture due to compressibility effects.

Findings

Small-scale enstrophy cascade remains intact

Large-scale energy flux loop forms with acoustic energy

Spectral slopes agree with theoretical predictions at small Mach numbers

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 $M\approx0.34$ 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.