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The inner-outer interaction model (Marusic, Mathis & Hutchins, Science, vol.329, 2010, 193-196) and the attached-eddy model (Townsend, Cambridge UniversityPress, 1976) are two fundamental models describing the multi-scale turbulenceinteractions and the organization of energy-containing motions in thelogarithmic region of high-Reynolds number wall-bounded turbulence,respectively. In this paper, by coupling the additive description with theattached-eddy model, the generation process of streamwise wall-shearfluctuations, resulting from wall-attached eddies, is portrayed. Then, byresorting to the inner-outer interaction model, the streamwise wall-shearstress fluctuations generated by attached eddies in a turbulent channel floware isolated. Direct comparison between the statistics from these two modelsdemonstrates that they are consistent to and complement each other. Meanwhile,we further show that the superpositions of attached eddies follow an additiveprocess strictly by verifying the validity of the strong and extended selfsimilarity. Moreover, we propose a Gaussian model to characterize theinstantaneous distribution of streamwise wall-shear stress, resulting from theattached-eddy superpositions. These findings are important for developing anadvanced reduced-order wall model.

journal of fluid mechanics

Consistency between the attached-eddy model and the inner-outer  interaction model: a study of streamwise wall-shear stress fluctuations in a  turbulent channel flow