Quasi-steady quasi-homogenous (QSQH) theory of the relationship between large-scale and small-scale motions in near-wall turbulence

The Quasi-Steady Quasi-Homogeneous (QSQH) theory describes the nature of the relationship between large-scale and small-scale structures in near-wall turbulent flows. In the present study, by introducing a notion of an ideal large-scale filter, the QSQH theory is stated in a rigorous form. A method is proposed for selecting a large-scale Fourier filter by multi-objective optimisation, with the first objective being a large correlation between large-scale fluctuations near the wall and in the layer at a certain finite distance from the wall, and the second objective being a small correlation between the small-scales in the same layers. The filter is demonstrated to give good results. Within the QSQH theory expansions in the amplitude of the large-scale fluctuations (assumed to be small) are found for a number of flow characteristics. Taking into account more terms of the expansion was demonstrated to improve the agreement between the theory and the results of direct numerical simulations available in the literature. It is proposed to use the QSQH theory for extrapolating the results of numerical and physical experiments from moderate to higher values of the Reynolds number. Two specific extrapolation methods based on the QSQH theory were developed, and their advantages and disadvantages explored. For near-wall region within about 100 wall units the accuracy of about 10% was achieved when extrapolating from the friction Reynolds number Reτ = 950 to Reτ = 4200. For using the technique in experiments, a special probe capable of measuring the large-scale motion, as it is defined in the QSQH theory, is required. Such a probe was designed and tested, so far in numerical simulations only. The main overall result of the present work is further validation of the QSQH theory and the development of the extrapolation method on its basis.Open Acces