The software implementation and applications of the quasi-steady-quasi-homogeneous (QSQH) theory in near-wall turbulence

The three-dimensional implementation of the Quasi-Steady-Quasi-Homogeneous-(QSQH) theory of scale interaction in near-wall turbulence has been integrated into an online software tool. This tool takes the wall friction distribution of a given flow as input and generates a set of velocity snapshots that exhibit statistics consistent with those predicted by QSQH theory, while simultaneously having the statistical characteristics of the large-scale component of the input wall friction field. Consequently, this tool facilitates straightforward calculation of QSQH predictions for various flow statistics without requiring any derivations. The application of this tool was demonstrated in a number of examples involving plane channel and circular pipe flows in the range of the friction Reynolds numbers from 1000 to 6000. These examples encompass investigations into the relative error associated with Taylor expansions in the amplitude of large-scale motions, the validity of the so-called ``QSQH hypotheses per se'', compliance of the large-scale motions with the QSQH theory, variations in Reynolds shear across different Reynolds numbers, and QSQH predictions of two-point correlations at distinct wall-parallel locations. It also included a study of the feasibility of employing the QSQH model for predicting changes in velocity statistics across flows characterized by varying geometry (channel and pipe) and Reynolds numbers. The examined statistics include mean velocity profiles, turbulence intensity profiles, Reynolds shear stress, skewness and flatness measures for velocity fluctuations, and two-point correlation coefficients. A modification of the QSQH theory was proposed to address mass and momentum transport within the mathematical framework of the theory, in particular to ensure the conservation of mass for large-scale velocity components, as well as the conservation of mean longitudinal momentum up to second-order terms in the Taylor expansions of stress terms defined by the QSQH theory.