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 T_w/T_r = 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.

中文翻译：

---

Ma∞= 8时高超声速湍流边界层密度与温度波动的相关性

壁面温度显着影响湍流边界层的密度与温度波动（ρ ′和T ′）之间的相关性。考虑具有壁对回收温度之比T _w / T _r分别为0.8和0.15的直接数值模拟数据库。采用拟合斜率法和二维相关法可视化相关行为。结果表明，在缓冲区中发现了不利的趋势和分离的相关结构，可以将其视为ρ ′和T的相关性的影响'。为了揭示相关性，进行了一些统计分析。这表明通过壁冷却可以抑制流动中的极端事件；同时，小规模波动加剧。波动的行为是由于平均涡流强度降低和旋涡结构半径增大所致。