Influence of random fluctuations in the Λ-effect on meridional flow and differential rotation

We present a mean field model based on the approach taken by Rempel 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 2 orders of magnitude. It is further found that the correlation length and timescale 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 timescales for the replenishment of differential rotation and meridional flow. We find that the timescale for the replenishment of differential rotation (∼10 years) is nearly 4 orders of magnitude longer than the timescale 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.