Is the turbulent wind in convective flows driven by fluctuations?

In this paper, a direct check is presented whether the turbulent wind in Rayleigh–Bénard convection is driven by turbulent Reynolds stresses, associated with the tilting plumes at the upper and the lower horizontal walls. This is done by evaluation of experimental data obtained from particle image velocimetry measurements in the centerplane of a cubic convection cell and two-dimensional solution of the Navier–Stokes equations in a square domain. Although, in both, there are regions of negative turbulent energy production P=−〈uiuj〉∂Ui/∂xj, meaning that, locally, energy is transferred from velocity fluctuations to the mean flow, the integral of turbulent energy production over the whole flow field is essentially positive. This implies that the turbulent wind is not driven by the turbulent Reynolds stresses. It is demonstrated from the numerical results that once the mean flow is established, the temperature of the fluid is larger at one side wall and smaller at the other and therefore, the mean flow is driven by the mean buoyant force at the side walls.