Countergradient diffusion of turbulent heat flux in turbulent Rayleigh flow

Motivated by countergradient diffusion phenomenon in the turbulent premixed flame, we discuss the effects of heat release on turbulence. We devised and implemented a direct numerical simulation of the turbulent Rayleigh flow generated by isotropic turbulence flowing into the Rayleigh flow. We show that countergradient diffusion of the turbulent heat flux occurs in the turbulent Rayleigh flow, and we discuss its mechanism based on the transport equations of the turbulent statistical quantities. It is shown that the released heat amplifies the density-internal energy correlation and contributes countergradient diffusion through the pressure gradient effect.