A data-driven quasilinear approximation for supersonic turbulent channel flow

This work models the compressibility effects in supersonic turbulent channel flow using the approach of data-driven quasi-linear approximation (DQLA) (Holford & Hwang, J. Fluid Mech., vol. 980, 2024, p.A12) proposed for incompressible channel flow. Full nonlinear equations are considered for time-averaged mean, and the fluctuations are linearised around the mean with the nonlinear term consisting of an eddy-viscosity model and stochastic forcing. The streamwise weight of the stochastic forcing is determined by matching the velocity spectra from DNS of incompressible flow and that produced by the eddy viscosity enhanced linearised compressible Navier-Stokes equations. The spanwise weights are determined self-consistently, so that mean density, momentum and temperature equations are satisfied with their prescribed properties. The proposed compressible data-driven quasi-linear approximation demonstrates the capability to produce turbulent intensity profiles and energy spectra that exhibit qualitatively similar behavior across the entire wall-normal domain as DNS data up to Ma=3, where Ma is the Mach number.