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The wall cooling effect on the spectra and structures of thermodynamicvariables are investigated in hypersonic turbulent boundary layers. The densityand temperature can be divided into the acoustic and entropic modes based onthe Kovasznay decomposition. The intensities of the pressure and the acousticmodes of density and temperature attain the maximum values near the wall, whilethose of the entropy and the entropic modes of density and temperature achievetheir primary peaks near the edge of boundary layer. In the near-wall region,the pressure and the acoustic modes of density and temperature aresignificantly enhanced when the wall is strongly cooled, which can beattributed to the appearance of the travelling-wave-like alternating positiveand negative structures. Moreover, the intensities of the entropy and theentropic modes of density and temperature become stronger near the wall as thewall temperature decreases, due to the appearance of the streaky entropicstructures. The streaky entropic structures are mainly caused by the advectioneffect of the strong positive wall-normal gradient of the mean temperatureassociated with ejection and sweep events. {It is also found that the profilesof the intensities of the entropy, density and temperature are similar to eachother far from the wall, which are mainly due to the reason that the entropicmodes are dominant in the fluctuating density and temperature in the far-wallregion. The acoustic modes of density and temperature only have significantcontributions in the near-wall region.

Wall cooling effect on spectra and structures of thermodynamic variables in hypersonic turbulent boundary layers