Auto-encoder-assisted analysis of amplitude and wavelength modulation of near-wall turbulence by outer large-scale structures in channel flow at friction Reynolds number of 5200

Abstract

The present paper reports a novel methodology that allows the intensity of, and the underlying mechanism for, the amplitude and length-scale modulation (amplification or attenuation) of the turbulent stresses in the boundary layer of a channel flow at Reτ=5200 to be clarified. A unique aspect of the present framework is the use of an auto-encoder algorithm to separate full-volume extremely large DNS fields into large-scale and small-scale motions. This approach is adopted in preference to the empirical mode decomposition (EMD) previously used by the present authors at the lower Reynolds number, Reτ=1000, because the resource requirements posed by the EMD quickly become untenable due to the extremely large direct numerical simulation (DNS) data set and the large solution box needed to capture the wide spectrum of scales at the present Reynolds number. A second original element is a formalism that derived the modulation, conditional on large-scale fluctuations, from continuous statistical quantities represented as multivariable-joint probability-density functions (\textit{pdfs}), thus obviating the need for any discrete representation or binning beyond that imposed by the discrete DNS solution. A third novel aspect is the use of the length-scale-wise derivative of the second-order structure function to quantify the modulation (increase or decrease) in the length scale, again conditional on the large-scale structures. Apart from illuminating the modulation itself, the study examined the validity of the Quasi-Steady Hypothesis which proposes that the near-wall turbulence is universal when scaled by the spatially and temporally varying large-scale wall shear stress, rather than its time average.