\gamma_\theta = \gamma_{0\theta} \left[1+\mathrm{erf}\left(\frac{r-0.8R_\odot}{0.55R_\odot}\right)\right]
\left[1-\mathrm{erf}\left(\frac{r-0.98R_\odot}{0.025R_\odot}\right)\right]
\times \cos \theta \sin^4 \theta ~~~~\end{aligned}$$ The value of $\gamma_{0r}$ and $\gamma_{0\theta}$ determines the amplitude of $\gamma_r$ and $\gamma_\theta$ respectively. Fig. 3 (top and bottom plot) shows that radial pumping speed (dashed lines) is negative throughout the convection zone corresponding to downward advective transport and vanishes below $0.7R_\odot$. The radial pumping speed is maximum near the poles and decreases towards the equator. Fig. 3 (top and bottom plot) shows that the latitudinal pumping speed (solid lines) is positive (negative) in the convection zone in the northern (southern) hemisphere and vanishes below the overshoot layer. This corresponds to equatorward latitudinal pumping throughout the convection zone.

Dynamo simulations with turbulent pumping generate solar-like magnetic cycles (Fig. 4 and Fig. 5). Now the toroidal field belt migrates equatorward, the solution exhibits solar-like parity and the correct phase relationship between the toroidal and poloidal components of the magnetic field (see Fig. 5). Evidently, the coupling between the poloidal source at the near-surface layers with the deeper layers of the convection zone where the toroidal field is stored and amplified, the equatorward migration of the sunspot-forming toroidal field belt and correct solar-like parity is due to the important role played 