SCALING LAWS AND WALL-ATTACHED STRUCTURES IN A SUPERSONIC TURBULENT CHANNEL FLOW

Abstract

To establish integrating explanation for characteristics of compressible wall-bounded turbulence, scaling laws and relevant turbulent coherent structures in compressible wall-bounded turbulence are investigated in light of Townsend's attached-eddy hypothesis. Using data of direct numerical simulation of supersonic turbulent channel flow between isothermal walls, we verified the scaling laws for mean velocity and Reynolds stresses, which can be predicted by attached-eddy hypothesis in a unified way. The transformed mean velocity profiles and the Reynolds stresses using semi-local scale supports the predicted scaling laws at certain extent. However, complete logarithmic dependence is not achieved due to relatively low-Reynolds number or insufficient scale separation, especially for streamwise normal stress. In search of coherent structures responsible for the logarithmic dependence of the turbulent statistics, wall-attached structures of velocity fluctuations are extracted from instantaneous flow fields. Reconstructed flow field from wall-attached self-similar structures fits more closer to the logarithmic variation. With these findings, we have provided the convincing evidence for the validity of the scaling laws and the existence of coherent structures corresponding the attached-eddy hypothesis for the compressible wall-bounded turbulence.