Interscale transport of Reynolds stresses in wall-bounded flows

Sammanfattning: Couette, pipe, channel, and zero-pressure gradient (ZPG) turbulent boundary layer (TBL) flows have classically been considered as canonical wall-bounded turbulent flows since their near-wall behavior is generally considered to be universal, i.e. invariant of the flow case and the Reynolds number. Nevertheless, the idea that large-scale motions, being dominant in regions further away from the wall, might interact with and influence small-scale fluctuations close to the wall has not been disregarded. This view was mainly motivated due to the observed failure of collapse of the Reynolds normal stresses in viscous scaling. While this top-down influence has been studied extensively over the last decade, the idea of a bottom-up influence (backward energy transfer) is less examined. One exception was the recent experimental work on a Couette flow by Kawata, T. & Alfredsson, P. H. (Phys. Rev. Lett. 120, 244501, 2018). In the present work, a spectral representation of the Reynolds Stress transport equation is used to perform a scale-by-scale analysis of the terms in the equation. Two flow cases were studied: first, a Direct Numerical Simulation (DNS) of a Couette flow at a similar Reynolds number as Kawata and Alfredsson. The Reynolds number was ReT = 120, viscosity v. Second, a Large Eddy Simulation (LES) of a ZPG TBL at ReT = 730, 1270, and 2400. For both cases the classic interscale transport or turbulent kinetic energy was observed. However, also an inverse interscale transport of Reynolds shear stress was observed for both cases.