On the validity of the quasi-steady-turbulence hypothesis in representing the effects of large scales on small scales in boundary layers

The “quasi-steady hypothesis,” as understood in the context of large-scale/small-scale interactions in near-wall turbulence, rests on the assumption that the small scales near the wall react within very short time scales to changes imposed on them by energetic large scales whose length scales differ by at least one order of magnitude and whose energy reaches a maximum in the middle to the outer portion of the log-law layer. A key statistical manifestation of this assumption is that scaling the small-scale motions with the large-scale wall-friction-velocity footprints renders the small-scale statistics universal. This hypothesis is examined here by reference to direct numerical simulation (DNS) data for channel flow at Reτ ≈ 4200, subjected to a large-scale/small-scale separation by the empirical mode decomposition method. Flow properties examined include the mean velocity, second moments, joint probability density functions, and skewness. It is shown that the validity of the hypothesis depends on the particular property being considered and on the range of length scales of structures included within the large-scale spectrum. The quasi-steady hypothesis is found to be well justified for the mean velocity and streamwise energy of the small scales up to y+∼𝒪(80), but only up to y+∼𝒪(30) for other properties.