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

Abstract

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 fulfil 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. 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 a way for investigating the multi-physics coupling in turbulence, and reinforcing our analysing and modelling capability to the interrelated problems.

Study of the linear models in estimating coherent velocity and temperature structures for compressible turbulent channel flows

“…2014). In a recent work, Cheng & Fu (2023 a ) note that the profile of turbulent Prandtl number in supersonic channels is very close to the incompressible case with heat transfer (Antonia, Abe & Kawamura 2009). They suggest that the coherent temperature fluctuations behave like a passive scalar, and the coupling between the velocity and temperature fields results largely from the advection effect.…”

“…Previous studies have verified that this set-up can capture most of the large-scale motions in the outer region (Agostini & Leschziner 2014). Readers can refer to Cheng & Fu (2022 b , 2023 a ) for more analyses on the DNS statistics. The case , (, ) is selected as the benchmark case for this study, which is of the highest and in our dataset.…”

“…Similar to that for , SLSE can be deployed to estimate given or . The latter combination concerns the coupling effects between and (Cheng & Fu 2023 a ). The two kernel functions are defined as …”

“…2023). Moreover, Cheng & Fu (2023 a ) point out that in the logarithmic region, only the scales corresponding to the attached eddies and VLSMs are firmly coupled; the Reynolds number acts as the crucial similarity parameter in constructing the coupling, rather than the Mach number.…”

“…Nevertheless, its application in compressible flows is still limited. Very recently, Cheng & Fu (2022 b , 2023 a ) extend the SLSE framework for compressible flows. The self-similarity of thermodynamic quantities and the coupling effects between velocity and temperature are thus investigated.…”