Reynolds number and wall cooling effects on correlations between the thermodynamic variables in hypersonic turbulent boundary layers

The Reynolds number and wall cooling effects on correlations between the thermodynamic variables are systematically investigated in hypersonic turbulent boundary layers by direct numerical simulations. The correlations between the thermodynamic variables and the streamwise velocity are also analysed. The Kovasznay decomposition is introduced to decompose the fluctuating density and temperature into the acoustic and entropic modes. It is found that in the strongly cooled wall cases, the travelling-wave-like alternating positive and negative structures (TAPNSs) are found in the fluctuating pressure and the acoustic modes of density and temperature, and the streaky entropic structures (SESs) are identified in the fluctuating entropy and the entropic modes of density and temperature near the wall. Furthermore, both the acoustic and the entropic modes of density and temperature give significant contributions to the correlations involving density and temperature in the near-wall region, while these correlations are almost totally contributed by the entropic modes in the far-wall region. The entropic modes of the density and temperature are almost linearly correlated with the fluctuating entropy. Therefore, the fact that the fluctuating entropy is strongly correlated with the fluctuating density and temperature far from the wall is mainly due to the dominance of the entropic modes in the fluctuating density and temperature. Moreover, the fluctuating temperature is strongly positively correlated with the fluctuating streamwise velocity near the wall in strongly cooled wall cases, which can be ascribed to the appearance of the TAPNSs and SESs.