A Babcock‐Leighton Flux Transport Dynamo with Solar‐like Differential Rotation

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Abstract
We investigate the properties of a kinematic —ux transport solar dynamo model. The model is charac- terized by a solar-like internal diÜerential rotation pro—le, a single-cell meridional —ow in the convective envelope that is directed poleward at the surface, and a magnetic diÜusivity that is constant within the envelope but decreases sharply at the core-envelope interface. As in earlier —ux transport models of the Babcock-Leighton type, we assume that the poloidal —eld is regenerated as a consequence of the emer- gence at the surface, and subsequent decay, of bipolar active regions exhibiting a systematic tilt with respect to the east-west direction. Inspired by recent simulations of the rise of toroidal magnetic —ux ropes across the solar convective envelope, we model this poloidal —eld regeneration mechanism as a nonlocal source term formulated in such a way as to account for some of the properties of rising —ux ropes revealed by the simulations. For a broad range of parameter values the model leads to solar cycle¨ like oscillatory solutions. Because of the solar-like internal diÜerential rotation pro—le used in the model, solutions tend to be characterized by time-latitude (butter—y) diagrams that exhibit both poleward- and equatorward-propagating branches. We demonstrate that the latitudinal shear in the envelope, often omitted in other —ux transport models previously published in the literature, actually has a dominant eÜect on the global morphology and period of the solutions, while the radial shear near the core- envelope interface leads to further intensi—cation of the toroidal —eld. On the basis of an extensive parameter space study, we establish a scaling law between the time period of the cycle and the primary parameters of the model, namely the meridional —ow speed, source coefficient, and turbulent diÜusion coefficient. In the parameter regime expected to characterize the Sun, we show that the time period of the cycle is most signi—cantly in—uenced by the circulation —ow speed and, unlike for conventional mean —eld a) dynamos, is little aÜected by the magnitude of the source coefficient. Finally, we present one speci—c solution that exhibits features that compare advantageously with the observed properties of the solar cycle. Subject headings: diÜusionSun: interiorSun: magnetic —eldsSun: rotation