Investigation of the inclination angles of wall-attached eddies for streamwise velocity and temperature fields in compressible turbulent channel flows

Townsend's attached eddy hypothesis (AEH), one of the most elegant models in incompressible wall turbulence, has been recently applied to compressible wall turbulence to explain the numerical observations and predict the scaling laws. Before a more profound extension can be established, a comprehensive investigation of the features of wall-attached eddies for streamwise velocity and temperature fields in compressible wall-bounded turbulence is required. In this work the AEH and the inner-outer interaction model [Marusic et al., Science 329, 193 (2010)] are combined to isolate the signature of attached eddies at a targeted length scale and then assess their inclination angles statistically based on the direct numerical simulation database. The inclination angle obtained in the streamwise velocity fluctuating fields, which approaches 45 as the Reynolds number increases, shows a minor Mach-number influence within the Mach-number range included in this work. As for those in temperature fluctuations, a high statistical similarity can be seen to streamwise velocity fluctuations. This slight Mach-number effect indicates that a uniform model can be potentially developed for compressible wall-bounded turbulence with different Mach numbers.