Quasisteady quasihomogeneous description of the scale interactions in near-wall turbulence

Abstract

By introducing the notion of an ideal large-scale filter, a formal statement is given of the hypothesis of the quasisteady quasihomogeneous nature of the interaction between the large and small scales in the near-wall part of turbulent flows. This makes the derivations easier and more rigorous. A method is proposed to find the optimal large-scale filter by multiobjective optimization, with the first objective being a large correlation between large-scale fluctuations near the wall and in the layer at a certain finite distance from the wall and the second objective being a small correlation between the small scales in the same layers. The filter is demonstrated to give good results. Within the quasisteady quasihomogeneous theory, expansions for various quantities are found with respect to the amplitude of the large-scale fluctuations. Including the higher-order terms improves the agreement with numerical data. Interestingly, it turns out that the quasisteady quasihomogeneous theory implies a dependence of the mean profile logarithmic-law constants on the Reynolds number. The main overall result of the present work is the demonstration of the relevance of the quasisteady quasihomogeneous theory for near-wall turbulent flows.