Conservative compressible one-dimensional turbulence formulation and application to high-Reynolds-number compressible turbulent channel flows

One-dimensional turbulence (ODT) is an efficient stochastic methodology for turbulent flow simulation with dimensionality reduction. In this study, the conservative compressible ODT model is further developed and applied to address the challenge of accurately and economically modeling high-Reynolds-number wall-bounded compressible turbulent flows. The prohibitively costly direct numerical simulation (DNS) of multiscale motions for fully developed compressible turbulent channel flows is replaced by a much more economical simulation using the conservative compressible ODT model. The quantitative accuracy in capturing the main turbulent features, including the first-order mean statistics and the second-order and third-order turbulent fluctuation statistics, is verified by comparing the ODT results with different canonical DNS results at Mab = 0.5, 1.5, and 3.0. With its accuracy tested, the proposed ODT model is employed to capture the turbulent features of fully developed channel flows at Reynolds numbers widely ranging from 6000 to 60 000. The proposed ODT model reproduces Reynolds number effects in turbulent fluctuation statistics at all three Mach numbers mentioned above. Furthermore, considering the correspondence between the statistical effect of multiscale eddy events stochastically sampled in ODT and the effect of actual multiscale turbulent motions, a mechanism for Reynolds number effects is revealed by analyzing interactions between the multiscale eddy events from the ODT perspective. Evidence shows that the large-eddy motions in the outer region, rather than the small ones in the inner region, contribute to the Reynolds number effects when all these motions are plotted in inner-scaled units.