Spectra scaling of velocity components and pressure–strain correlations for hypersonic boundary layers at a range of wall-to-recovery temperatures

Abstract

Flow similarity is one of the most desirable features for turbulence under different conditions. For hypersonic boundary layers, different wall temperatures are known to change the turbulence evolution by influencing the intercomponent energy transfer, while the flow similarity has received less attention. Based on direct numerical simulations, this work investigates the spectral distribution of velocity components and pressure–strain correlations for hypersonic boundary layers at Mach 6 and wall-to-recovery temperature ratios equal to 0.3, 0.5, 0.76, and 1. The wall-normal evolution of turbulent structures is compared by the spectra peak scale λSP, wall-normal location ySP, and the vertical profiles of peak scale λP. For all cases, the peak scale profiles exhibit linear increases with a height of 0.1≤y/δ≤0.25. The linear growth of the turbulence scale in the logarithmic region indicates the existence of self-similar structures, and the agreement of peak scales in the outer scaling suggests the flow similarity under different wall temperatures. Likewise, the streamwise pressure–strain term has the peak scale profile linearly dependent on the height for the same vertical range 0.1≤y/δ≤0.25 with velocity components, while the wall-normal and spanwise terms exhibit both linear and constant vertical dependence depending on the wall temperatures. With the increase in wall temperature, the peak scale exhibits broader constant vertical dependence and narrower linear vertical dependence. The cospectral analysis further confirms that the pressure–strain correlations are maximized at different spanwise-vertical aspect ratios of turbulence structures.