Prediction of the phase difference between large-scale velocity and Reynolds stress fluctuations in wall turbulence

A resolvent-based model was used to predict the phase-difference profile between velocity and stress coherent motions measured in a high Reynolds number channel flow as a proxy for predicting large-and small-scale turbulent interactions. The resolvent model is based on the transfer-function approach for scale interactions in wall turbulence proposed in Jacobi et al. (J. Fluid Mech., vol 914, 2021, pp. 1-27), but incorporates a quasi-empirical weighting scheme to construct composite mode shapes that represent the realistic dispersion of convection velocities associated with the large scales of turbulence. The weighting scheme was derived from the observed similarity between the spectral region where the resolvent operator is low rank and the streamwise spectral energy density of wall-bounded turbulence, and was found to be superior to both single-convection velocity models and models based on linearly weighted modes, when compared with cross-spectral phase calculations from a channel flow computation. The ability to predict the phase relationship between large-scale coherent motions and their associated stress fluctuations allows for refining and extending resolvent-based models of turbulence to describe small-scale features of wall-bounded flows.