Correlation between density and temperature fluctuations of hypersonic turbulent boundary layers at Ma∞ = 8

The correlation between density and temperature fluctuations (ρ′ and T′) of the turbulent boundary layer is significantly affected by wall temperature. Direct numerical simulation databases with the ratio of wall-to-recovery temperature Tw/Tr = 0.8 and 0.15 are considered. A fitting slope method and a two-dimensional correlation method are adopted to visualize the correlated behavior. The results show that an adverse trend and a separated correlated structure are found in the buffer region, which can be treated as the effects of the correlation of ρ′ and T′. To reveal the correlation, several statistical analyses are conducted. It indicates that the extreme events in the flow are suppressed with wall cooling; meanwhile, the small-scale fluctuations are enhanced. The behavior of the fluctuations results from the reduced mean swirling strength and the increased radius of the vortical structures.