Time-dependent viscosity, dissipation, and the turbulent cascade

Rapid changes to the mean temperature result in corresponding changes in the molecular viscosity. The viscosity, in turn, will effect the dissipation rate, throwing the turbulence out of equilibrium, and requiring a subsequent relaxation back to an equilibrium state. This is an important process in numerous engineering problems, including internal combustion engines (heating due to compression and combustion) and turbulence passing through a shock. Using direct-numerical simulation of incompressible turbulence with a time-dependent viscosity, we can observe the effect of both the initial viscosity change and the subsequent return to equilibrium. Considering both the spectra and higher-order statistics we can identify some key issues for future model improvements.