  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.
