Predicting the response of small-scale near-wall turbulence to large-scale outer motions

A phenomenological model is provided, based on post-processing Direct Numerical Simulation (DNS) data at Reτ = 1020, which permits the near-wall-turbulence statistics to be predicted from a “universal signal,” free from the effects of large-scale motions, in combination with information on the large-scale motions in the outer log-law region. The separation of large-scale and small-scale motions is effected, unusually, by means of the “Empirical Mode Decomposition” method, without explicit wavelength cutoffs. The model first yields the universal field by removing, from a full-volume turbulence field at an arbitrary time level, the effects of large-scale convective displacements (footprints), the modulation of the small-scale motions, caused by the large-scale motions, and distortions arising from sweep-induced splatting. In contrast to other modelling efforts, the present framework extends to all three velocity components, as is demonstrated by reference to joint (u − v) and (u − w) probability-density functions (PDFs). The model is then successfully used to reconstitute the full near-wall statistics by combining the universal field with the outer large-scale motions at any time level other than that for which the universal field was determined.