  We present a mean field model based on the approach taken by Rempel
(astro-ph/0604451) in order to investigate the influence of stochastic
fluctuations in the Reynolds stresses on meridional flow and differential
rotation. The stochastic fluctuations found in the meridional flow pattern
directly resemble the stochastic fluctuations of the Reynolds stresses, while
the stochastic fluctuations in the differential rotation are smaller by almost
two orders of magnitude. It is further found that the correlation length and
time scale of the stochastic fluctuations have only a weak influence on
meridional flow, but a significant influence on the magnitude of variations in
the differential rotation. We analyze the energy fluxes within the model to
estimate time scales for the replenishment of differential rotation and
meridional flow. We find that the time scale for the replenishment of
differential rotation (~10 years) is nearly four orders of magnitude longer
than the time scale for the replenishment of meridional flow, which explains
the differences in the response to stochastic fluctuations of the Reynolds
stress found for both flow fields.
