Streamwise velocity and temperature coupling in compressible turbulent channel flow: Correlation and streak overlap analysis

This paper employs direct numerical simulation to systematically investigate the correlation between velocity and temperature in compressible turbulent channel flows at Mach numbers 0.5, 1.5, and 3.0. The mean and fluctuating velocity and temperature fields are analyzed using relevant statistical measures. In addition to conventional statistics of velocity–temperature correlation, an image recognition algorithm based on the Intersection Over Union (IOU) metric is introduced to analyze the overlapping characteristics of near-wall streaks, enabling quantitative characterization of the overlap ratio between low-velocity and low-temperature streaks. The results show that in the near-wall region, velocity and temperature fluctuations exhibit a strong positive correlation modulated by coherent structures. In the outer region, however, large-scale temperature structures lack the self-sustaining mechanism inherent to velocity streaks, resulting in a significant weakening of their correlation. IOU analysis quantitatively reveals a high degree of spatial overlap between low-velocity and low-temperature streaks near the wall. The magnitude and wall-normal variation of the IOU closely follow those of the correlation coefficient RuT, confirming that the strong coherence in streak morphology is the physical origin of the high correlation between velocity and temperature fluctuations. This finding also provides a mechanistic explanation for the synchronous decay of IOU and RuT with increasing wall distance. Moreover, the streak spacing increases with Mach number when expressed in wall units but collapses to an approximately constant value of around 100 under semi-local scaling.