Comparisons between the first- and second-order spectral stochastic estimations in investigating the multiphysics couplings for a supersonic turbulent channel flow

It is generally believed that the thermodynamic and velocity fields are highly coupled in compressible wall-bounded turbulence. In the present study, we employ the second-order spectral stochastic estimation (SSSE) to investigate the scaling behaviors of the couplings between these fields, which include the velocity-temperature (u-T ) and velocity-pressure (u-p) couplings. Particular attention is paid to the differences between the SSSE and the first-order spectral stochastic estimation (FSSE). Spectral analyses of the couplings in the logarithmic region suggest that the linear part of the u-T coupling is strong at the scales corresponding to the energy-containing motions populating the same locus, whereas the quadratic term is centered at the scales corresponding to the very large-scale motions. In contrast, the linear component of the u-p coupling shows a stronger isotropic behavior, whereas the quadratic component is located at the large spanwise scales. Several metrics are proposed to compare the accuracy of the FSSE and the SSSE in estimating the thermodynamic fields with the velocity input in the logarithmic region. The SSSE has an advantage over the FSSE in estimating the strong events and the variation tendencies of thermodynamic fields. As a result, the distributions of the estimated fields by the SSSE are closer to those of the raw fields. However, the abilities of the FSSE and the SSSE in capturing the transient characteristics of the near-wall thermodynamic fields are limited and of little difference, with the velocity field in the logarithmic region as input. Only the low-pass filtered signals can be recovered. The present work uncovers details about the multiphysics couplings in compressible wall turbulence.