Scale-by-Scale energy transfer in in-homogeneous turbulent flows

Abstract

In this work, we study the scale-by-scale energy transfer in inhomogeneous turbulence. In particular, we consider the case of wall-bounded thermally-stratified turbulent channel flow, and the case of a free-surface turbulent (open) channel flow. For the thermally-stratified turbulent channel flow, we analyze a database obtained by Direct Numerical Simulations (DNS) performed at two different values of the shear Reynolds number, Re = 180 and Re = 1000, and different values of the shear Richardson number (which quantifies the importance of the thermal stratification compared to inertia). Specifically, we used Ri = 25 and Ri = 50 for Re = 180, and Ri = 50 for Re = 1000. We applied our analysis to a wall-parallel plane located at the center of the channel, where internal gravity waves are observed.For the free-surface turbulent channel flow, we analyze a database obtained by Direct Numerical Simulations (DNS) performed at three different values of the shear Reynolds number, Re = 180, Re = 1000 and Re = 6000.Current results seem to indicate that the local value of the energy flux can often be negative – which indicates a local inverse energy cascade – while the average flux remains positive, which indicates an overall direct energy cascade. This is observed across all scales and for all cases considered here, even for the very large Reynolds numbers.