The solar activity cycle is successfully modeled by the flux transport dynamo, in which the meridional circulation of the Sun plays an important role. Most of the kinematic dynamo simulations assume a one-cell structure of the meridional circulation within the convection zone, with the equatorward return flow at its bottom. In view of the recent claims that the return flow occurs at a much shallower depth, we explore whether a meridional circulation with such a shallow return flow can still retain the attractive features of the flux transport dynamo (such as a proper butterfly diagram, the proper phase relation between the toroidal and poloidal fields). We consider additional cells of the meridional circulation below the shallow return flow-both the case of multiple cells radially stacked above one another and the case of more complicated cell patterns. As long as there is an equatorward flow in low latitudes at the bottom of the convection zone, we find that the solar behavior is approximately reproduced. However, if there is either no flow or a poleward flow at the bottom of the convection zone, then we cannot reproduce solar behavior. On making the turbulent diffusivity low, we still find periodic behavior, although the period of the cycle becomes unrealistically large. Also, with a low diffusivity, we do not get the observed correlation between the polar field at the sunspot minimum and the strength of the next cycle, which is reproduced when diffusivity is high. On introducing radially downward pumping, we get a more reasonable period and more solar-like behavior even with low diffusivity.

We develop a three-dimensional kinematic self-sustaining model of the solar dynamo in which the poloidal field generation is from tilted bipolar sunspot pairs placed on the solar surface above regions of strong toroidal field by using the SpotMaker algorithm, and then the transport of this poloidal field to the tachocline is primarily caused by turbulent diffusion. We obtain a dipolar solution within a certain range of parameters. We use this model to study the build-up of the polar magnetic field and show that some insights obtained from surface flux transport (SFT) models have to be revised. We present results obtained by putting a single bipolar sunspot pair in a hemisphere and two symmetrical sunspot pairs in two hemispheres.We find that the polar fields produced by them disappear due to the upward advection of poloidal flux at low latitudes, which emerges as oppositely-signed radial flux and which is then advected poleward by the meridional flow. We also study the effect that a large sunspot pair, violating Hale's polarity law would have on the polar field. We find that there would be some effect-especially if the anti-Hale pair appears at high latitudes in the mid-phase of the cycle-though the effect is not very dramatic.

Using different proxies of solar activity, we have studied the following features of solar cycle. (i) A linear correlation between the amplitude of cycle and its decay rate, (ii) a linear correlation between the amplitude of cycle n and the decay rate of cycle (n−1) and (iii) an anti-correlation between the amplitude of cycle n and the period of cycle (n − 1). Features (ii) and (iii) are very useful because they provide precursors for future cycles. We have reproduced these features using a flux transport dynamo model with stochastic fluctuations in the Babcock-Leighton α effect and in the meridional circulation. Only when we introduce fluctuations in meridional circulation, we are able to reproduce different observed features of solar cycle. We discuss the possible reasons for these correlations.