A thorough understanding of wall-bounded turbulence has long been a central research topic in fluid dynamics. Resolvent analysis has been proven effective at qualitatively capturing key features of turbulent coherent structures in both wall-bounded and free shear flows, particularly when nonlinear forcing is approximated as white noise. However, in turbulent systems where the response is typically not low rank, the nontrivial structure of nonlinear forcing can induce considerable discrepancies between resolvent modes and data-derived modal features. To enhance the predictive capability of resolvent models, a rigorous closure of the nonlinear forcing term is therefore essential. In this study, fully resolved direct numerical simulations are used to study coherent structures in turbulent channel flow under subsonic and supersonic conditions. To quantitatively improve the performance of linear resolvent analysis, the effects of nonlinear forcing are incorporated through both a compressible eddy-viscosity model and a data-driven approach. Both the compressible eddy-viscosity model and the optimized eddy-viscosity field obtained from the data-driven approach yield a significant improvement in modal alignments between resolvent and spectral proper orthogonal decomposition modes, achieving a consistency of over 90% for both near-wall and large-scale coherent structures. To further boost predictive capability, a scaling factor is subsequently introduced into the compressible eddy-viscosity model. Calibration of a single constant parameter consistently yields improved predictions relative to the original compressible eddy-viscosity model, holding great promise for enhancing the predictive accuracy of coherent structures in compressible turbulent flows.

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• Channel flow
• Compressible turbulence
• Direct numerical simulations