Vertical coherence of pressure and velocity structures in hypersonic turbulent boundary layers

Understanding the vertical coherence of the pressure structure and its interaction with velocity fields is critical for elucidating the mechanisms of acoustic generation and radiation in hypersonic turbulent boundary layers. This study employs linear coherence analysis to examine the self-similar coherent structures in the velocity and pressure fields within a Mach 6 hypersonic boundary layer, considering a range of wall-to-recovery temperature ratios. The influence of wall cooling on the geometric characteristics of these structures, such as inclination angles and three-dimensional aspect ratios, is evaluated. Specifically, the streamwise velocity exhibits self-similar coherent structures with the streamwise/wall-normal aspect ratio ranging from 16.5 to 38.7, showing a linear increases with decreasing wall temperatures. Similar linear dependence between the streamwise/wall-normal aspect ratio and the wall temperatures are observed for the Helmholtz-decomposed streamwise velocity and the pressure field. In terms of velocity–pressure coupling, the solenoidal component exhibits stronger interactions with the pressure fields in the near-wall region, while the dilatational component has stronger interactions with the pressure field at large scales with the increase of height. Such coupling generally follows the distance-from-the-wall scaling of the pressure field, except in cooled wall cases. Using the linear stochastic estimation, the pressure field across the boundary layer is predicted by inputting the near-wall pressure/velocity signal along with the transfer kernel. The result demonstrates that near-wall pressure signals provide the most accurate description of the pressure field in higher regions of the boundary layer. As wall-mounted sensors can measure near-wall pressure fluctuations, this study presents a potential approach to predict the off-wall pressure field correlated with the near-wall structures based on wall-pressure measurements.