Energy cascade in variable-density jets
“Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity.” – Lewis F. Richardson (1922).
The poem by Richardson encapsulates one of the most celebrated idea in the phenomenological modeling of constant-density turbulence – the existence of an inertial subrange where energy cascades down from one turbulent eddy to another in a scale-local manner with a constant energy flux.
The situation is observed to change in a variable-density, non-Boussinesq turbulent SF6 jet where the small turbulent eddies were stretched by the mean flow gradients to become larger and carried with them the energy back to the mean flow (large eddies). Also, the nonlinear interscale energy cascade (a result connected to the vortex-stretching mechanism) was strengthened by the variable-density effect.
These conclusions were drawn by generalizing the von Karman-Howarth-Monin (KHM) equation to include variable-density effects, and subsequently applying the equation to an experimental dataset.
Lai, C.C.K., Charonko, J.J. and Prestridge, K. (2018). A Karman-Howarth-Monin equation for variable-density turbulence, Journal of Fluid Mechanics, 843:382-418.