Dependence of heat transport on the strength and shear rate of prescribed circulating flows

Abstract

We study numerically the dependence of heat transport on the maximum velocity and shear rate of physical circulating flows, which are prescribed to have the key characteristics of the large-scale mean flow observed in turbulent convection. When the side-boundary thermal layer is thinner than the viscous boundary layer, the Nusselt number (Nu), which measures the heat transport, scales with the normalized shear rate to an exponent 1/3. On the other hand, when the side-boundary thermal layer is thicker, the dependence of Nu on the Peclet number, which measures the maximum velocity, or the normalized shear rate when the viscous boundary layer thickness is fixed, is generally not a power law. Scaling behavior is obtained only in an asymptotic regime. The relevance of our results to the problem of heat transport in turbulent convection is also discussed.