Intermittency in Solar Cycle Caused by Stochastic Fluctuation in Meridional Circulation

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We present here how the stochastic fluctuation in meridional circulation can cause variation in amplitude and phase of the solar cycle as often observed as a long-term variability in the butterfly diagram. It has been shown by various authors that a kinematic, flux-transport dynamo with meridional circulation is capable of reproducing a majority of surface magnetic features. The scaling law, proposed on the basis of detail parameter space survey, suggests that the time-period of cycle is largely governed by flow speed. Since meridional circulation is a weak flow, vigorous convections could perturb this flow randomly by causing a stochastic fluctuation in its magnitude. Surface observations suggest variation of flow speed with time, while simulations suggest up to 100% fluctuation in amplitude of the flow in deep convection zone also. Assuming a correlation length in the streamlines comparable to dimension of granules and treating the correlation time (tau_c ) between two fluctuating flows and the amplitude of the fluctuating component as parameters, we show that the long-term variability in the amplitude of the solar cycle is most sensitive to the amplitude of the stochastic fluctuation in meridional circulation, but not so sensitive to tau_c . On the other hand, the longer tau_c affects the time-period, though not violating the so-called "phase locking" of the solar cycle, since we always find that whenever there occur a few short cycles, a few compensating longer cycles also occur to adjust the solar clock again. The National Center for Atmospheric Research is sponsored by the National Science Foundation.

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