On the Relation between Small-scale Intermittency and Shocks in Turbulent Flows

Abstract

High Reynolds number turbulence is characterized by extreme fluctuations of velocity gradients which can interact with shock waves in compressible flows. While these processes are traditionally thought to happen at very disparate range of scales, both turbulence gradients as well as shock gradients become stronger as the Reynolds number increases. Our interest here is to in- vestigate their relation in the high-Reynolds number limit. Our conclusion is that for intermittent turbulence with inertial range scaling exponents which grow more slowly than linear at asymptotically high orders, small-scale intermittency produces gradients which are commensurate with shocks. This result is interpreted in the context of shock-turbulence interactions where intermittency appears to be responsible, in part, for the holes observed in shocks from simulations and experiments. This effect is aided by the correlation between strong gradients and flow retardation ahead of the shock which is observed from analysis of our direct numerical simulation database of incompressible and compressible turbulence.