The correlations between the thermodynamic variables in hypersonic turbulent boundary layers of a lifting body

The correlations between thermodynamic variables in hypersonic turbulent boundary layers around a lifting body are comprehensively investigated through direct numerical simulations. By utilizing the Kovasznay decomposition, the fluctuating density and temperature are decomposed into acoustic and entropic modes. The traveling-wavelike alternating positive and negative structures are identified for the fluctuating pressure and acoustic modes of density and temperature, whereas the streaky structures are observed in the fluctuating entropy and entropic modes of the density and temperature near the wall. Both the acoustic and entropic modes of density and temperature make a significant contribution to the correlations of these variables in the near-wall region, whereas the entropic modes play a predominant role in the far-wall region. The strong correlation between fluctuating entropy and fluctuating density and temperature in the far-wall region is primarily attributed to the dominance of the entropic modes in these variables. The statistical properties and correlations of thermodynamic variables in the windward vortex region exhibit noticeable variations along the streamwise direction, characterized by an increase in entropy modes and decrease in acoustic modes. By contrast, the windward cross-flow region demonstrates stronger isotropy than the windward vortex region, as evidenced by minimal variations in the fluctuations and correlation coefficients of thermodynamic variables along the streamwise direction.