Wall-attached temperature structures in supersonic turbulent boundary layers

Abstract

It is well known that low- and high-speed velocity streaks are statistically asymmetric. However, it is unclear how different the low- and high-temperature structures (T-structures) are even though they are strongly coupled with the streamwise velocity. Therefore, this paper identifies three-dimensional wall-attached temperature structures in supersonic turbulent boundary layers over cooled and heated walls (coming from direct numerical simulations) and separates them into positive and negative families. Wall-attached T-structures are self-similar; especially, the length and width of the positive family are linear functions of the height. The superposed temperature variance in both positive and negative families exhibits a logarithmic decay with the wall distance, while the superposed intensity of the wall-normal heat flux in the negative family shows a logarithmic growth. The modified strong Reynolds analogy proposed by Huang, Coleman, and Bradshaw [“Compressible turbulent channel flows: DNS results and modelling,” J. Fluid Mech. 305, 185–218 (1995)] is still valid in the negative family. The relative position between T-structures of opposite signs depends on the wall temperature and that in the cooled-wall case differs significantly from the relative position between low- and high-speed streaks, especially those tall ones. In the cooled-wall case, although positive temperature fluctuations below and above the maximum of the mean temperature can cluster to large-scale wall-attached structures, they are very likely dynamically unrelated.