Linear-model-based study of the coupling between velocity and temperature fields in compressible turbulent channel flows

It is generally believed that the temperature and the velocity fields are highly coupled in compressible wall-bounded turbulence. In the present study, we employ a linear model, i.e., the two-dimensional spectral linear stochastic estimation (SLSE), to study this coupling from the perspective of the multi-scale energy-containing eddies. Particular attention is paid to the relevant statistical characteristics of the temperature field. The connections of the two fields are found to be varied with the wall-normal position in the boundary layer. In a nutshell, their entanglement is strongest in the near-wall region, and only the extreme thermal events cannot be captured by SLSE. In the logarithmic region, only the scales that correspond to the attached eddies and the very large-scale motions (VLSMs) are firmly coupled. The near-wall footprints of the former are organized in an additive manner and fulfill the predictions of the celebrated attached-eddy model. In the outer region, the two fields are linearly coupled only at the scales corresponding to VLSMs. These findings are demonstrated to be insensitive to the Mach number effects and ascribed to the similarity between the momentum and the heat transfer in compressible wall turbulence. And it is also shown that it is the Reynolds number rather than Mach number that acts as a key similarity parameter in constructing their coupling. The framework built in the present study may pave way for investigating the multi-physics coupling in turbulence, and reinforcing our analyzing and modelling capability to the interrelated problems.

Effects of mean shear on the vortex identification and the orientation statistics

This work compares the threshold applied to the swirling strength as well as the vortex orientation statistics in the total and fluctuating velocity fields using direct numerical simulations of compressible and incompressible turbulent channel flows. It is concluded that the difference in the swirling strength for vortex identification is minimal in the logarithmic region such that these two situations share the same threshold. Regarding the vortex orientation, the inclination angle remains similar. However, as the wall-normal distance increases, a more and more obvious distinction is noticed for its orientation with respect to the spanwise ($z$) direction. It is mainly due to their intrinsic differences and attendant contrasting preference, i.e., $-z$ direction for the total velocity field and $z$ direction for the fluctuating one. These observations function as a reasonable explanation for various remarks in previous studies.