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Long-term sunspot observations and solar activity reconstructions reveal thatthe Sun occasionally slips into quiescent phases known as solar grand minima,the dynamics during which is not well understood. We use a flux transportdynamo model with stochastic fluctuations in the mean-field andBabcock-Leighton poloidal field source terms to simulate solar cyclevariability. Our long-term simulations detect a gradual decay of the polarfield during solar grand minima episodes. Although regular active regionemergence stops, compromising the Babcock-Leighton mechanism, weak magneticactivity continues during minima phases sustained by a mean-field$\alpha$-effect; surprisingly, periodic polar field amplitude modulationpersist during these phases. A spectral analysis of the simulated polar fluxtime series shows that the 11-year cycle becomes less prominent while highfrequency periods and periods around 22 years manifest during grand minimaepisodes. Analysis of long-term solar open flux observations appears to beconsistent with this finding. Through numerical experimentation we demonstratethat the persistence of periodic amplitude modulation in the polar field andthe dominant frequencies during grand minima episodes are governed by the speedof the meridional plasma flow -- which appears to act as a clock.

Evidence of persistence of weak magnetic cycles driven by meridional plasma flows during solar grand minima phases