Turbulent energy transfers in physical and scale spaces at dissipative length scales

Abstract

In statistically stationary homogeneous incompressible turbulence, the average energy transfer rate balance which exists at diffusion/dissipation-dominated length scales does not reflect what actually happens locally in space and time. We use a highly resolved direct numerical simulation of forced periodic turbulence to shed some light on the actual fluctuating dynamics which occur at these very small scales and which are rubbed off by averaging. Even though the viscous diffusion in physical space averages to zero and fluctuates less intensely than all other terms (except the energy input rate) in the local (in space–time) two-point energy balance, it fundamentally cannot be neglected. The local unsteadiness and the interspace turbulence transport terms cannot be ignored either in the interscale energy dynamics in spite of the fact that they also average to zero.