Restricted Nonlinear Scale Interactions at High Reynolds Numbers

Restricted nonlinear (RNL) dynamics comprise a streamwise constant mean flow interacting with a dynamically restricted perturbation field. This model has been shown to capture key aspects of wall-turbulence including low order statistics and roll/streak interactions of the self-sustaining process at moderate Reynolds numbers. In this work we illustrate that the interpretation of the RNL dynamics as the evolution of a large-scale streamwise mean component interacting with small-scale perturbations is consistent with a similar scale decomposition of DNS data. This analysis allows us to evaluate the role of an additional streamwise-varying scale that captures additional scale interactions known to operate at higher Reynolds number turbulence. Augmenting the large-scale dynamics with this intermediate scale enables the recovery of accuracy of low-order statistics. The large-scale streamwise mean in this augmented RNL (ARNL) framework acts as a long train concatenated by turbulent bulges represented by the newly added streamwise varying large-scale. This ARNL model captures the foot-print of this large-scale on the small-scale structures near the wall. The results also show evidence of amplitude modulation of the small-scales, consistent with observations reported in the literature.