A hybrid data-driven explicit algebraic subgrid-scale closure for improved inter-scale energy transfer and turbulence structure prediction

The explicit algebraic (EA) subgrid-scale (SGS) closure is shown to overpredict inter-scale energy transfer in turbulent channel flow, leading to excessive SGS dissipation, attenuation of turbulence fluctuations, and degradation of flow statistics. The SGS kinetic energy, KSGS, is identified as the key modeling variable in EA closure, as it determines the SGS timescale, controls SGS dissipation, and scales the nonlinear stress contributions. In this regard, the currently employed dynamic equilibrium KSGS model is identified as a key component of the coupled EA closure, whose limitations propagate through the SGS timescale and nonlinear stress coefficients, leading to less accurate prediction of the inter-scale energy transfer and turbulence statistics. To address this deficiency, a hybrid physics–machine-learning framework is developed in which a deep neural network, trained on filtered direct numerical simulation data at Reτ=381 and two filter scales, is proposed to predict KSGS, while the algebraic structure of the SGS model is fully retained. The proposed model is assessed through both a priori and a posteriori analyses at friction Reynolds numbers up to Reτ=2000. The improved prediction of KSGS improves the balance between turbulent kinetic energy production and dissipation, reduces the artificially diffused streamwise Reynolds stress, and improves the underprediction of the mean velocity in the buffer layer. Corresponding improvements in energy spectra, two-point velocity correlations, and integral length scales demonstrate an improved representation of turbulence structure. The results show that enhanced modeling of KSGS is fundamental to restoring inter-scale energy transfer and turbulence structure in EA SGS closures, providing an effective hybrid framework that remains robust across a wide range of Reynolds numbers.