  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.
