Flux Correlations in Supersonic Isothermal Turbulence

TL;DR

This paper tests an analytically derived flux relation in supersonic isothermal turbulence using large-scale simulation data, finding reasonable agreement despite differences in turbulence driving mechanisms.

Contribution

It introduces a new approximate flux relation applicable to turbulence driven by large-scale acceleration, extending previous theoretical results.

Findings

The flux relation is validated against simulation data.

The new relation shows reasonable agreement with observed turbulence.

Results suggest applicability to astrophysical flows.

Abstract

Using data from a large-scale three-dimensional simulation of supersonic isothermal turbulence, we have tested the validity of an exact flux relation derived analytically from the Navier--Stokes equation by Falkovich, Fouxon and Oz [2010 New relations for correlation functions in Navier--Stokes turbulence. J. Fluid Mech. 644, 465]. That relation, for compressible barotropic fluids, was derived assuming turbulence generated by a large-scale force. However, compressible turbulence in simulations is usually initialized and maintained by a large-scale acceleration, as in gravity-driven astrophysical flows. We present a new approximate flux relation for isothermal turbulence driven by a large-scale acceleration, and find it in reasonable agreement with the simulation results.