Universality of the internal-to-kinetic energy conversion rate

Determine whether the mean conversion rate from internal energy to kinetic energy by compressions and expansions, expressed nondimensionally as $C_{I\rightarrow E}H^4/\nu^3$ in three-dimensional weakly compressible Rayleigh–Bénard convection, depends only on the Rayleigh and Prandtl numbers rather than on additional thermodynamic properties of the fluid.

Background

The paper argues that, in weakly compressible three-dimensional convection, the kinetic energy is forced by the conversion of internal energy into kinetic energy through compressions and expansions. For the Reynolds number to depend only on $Ra$ and $Pr$, as in the standard Boussinesq formulation, the nondimensional conversion rate $C_{I\rightarrow E}H^4/\nu^3$ must likewise be a function only of those two parameters.

The author explicitly states that it is unknown whether this universality is plausible. Resolving the issue would establish whether additional thermodynamic parameters—such as properties related to the ratio of specific heats—must enter the description of statistically stationary convection.