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In recent years, scale-by-scale energy transport in wall turbulence has beenintensively studied, and the complex spatial and interscale transfer ofturbulent energy has been investigated. As the enhancement of heat transfer isone of the most important aspects of turbulence from an engineeringperspective, it is also important to study how turbulent heat fluxes aretransported in space and in scale by nonlinear multi-scale interactions in wallturbulence as well as turbulent energy. In the present study, the spectraltransport budgets of turbulent heat fluxes are investigated based on directnumerical simulation data of a turbulent plane Couette flow with a passivescalar heat transfer. The transport budgets of spanwise spectra of temperaturefluctuation and velocity-temperature correlations are investigated in detail incomparison to those of the corresponding Reynolds stress spectra. Thesimilarity and difference between those scale-by-scale transports arediscussed, with a particular focus on the roles of interscale transport andspatial turbulent diffusion. As a result, it is found that the spectraltransport of the temperature-related statistics is quite similar to those ofthe Reynolds stresses, and in particular inverse interscale transfer iscommonly observed throughout the channel in both transport of the Reynoldsshear stress and wall-normal turbulent heat flux

Spectral analysis on transport budgets of turbulent heat fluxes in plane Couette turbulence