It is proposed that the observed near-surface inflows towards the active regions and sunspot zones provide a nonlinear feedback mechanism that limits the amplitude of a Babcock-Leighton-type solar dynamo and determines the variation of the cycle strength .
This hypothesis is tested with surface flux transport simulations including converging latitudinal flows that depend on the surface distribution of magnetic flux .
The inflows modulate the build-up of polar fields ( represented by the axial dipole ) by reducing the tilt angles of bipolar magnetic regions and by affecting the cross-equator transport of leading-polarity magnetic flux .
With flux input derived from the observed record of sunspot groups , the simulations cover the period between 1874 and 1980 ( corresponding to solar cycles 11 to 20 ) .
The inclusion of the inflows leads to a strong correlation of the simulated axial dipole strength during activity minimum with the observed amplitude of the subsequent cycle .
This in agreement with empirical correlations and in line with what is expected from a Babcock-Leighton-type dynamo .
The results provide evidence that the latitudinal inflows are a key ingredient in determining the amplitude of solar cycles .