Heat flux in Rayleigh–Bénard convection

We calculate the heat conductivity of the turbulence induced in the Rayleigh–Bénard convection. We show that the heat conductivity becomes large as we increase the temperature difference between the top and the bottom plates, i.e., the strength of the turbulence. We can easily see that the heat conductivity diverges in the transition regime from soft turbulence to hard turbulence as we can see in the viscosity coefficient in the same system.