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We propose a self-consistent explanation of Rieger-type periodicities, the Schwabe cycle, and the Suess-de Vries cycle of the solar dynamo in terms of resonances of various wave phenomena with gravitational forces exerted by the orbiting planets. Starting on the high-frequency side, we show that the two-planet spring tides of Venus, Earth, and Jupiter are able to excite magneto-Rossby waves, which can be linked with typical Rieger-type periods. We argue then that the 11.07-year beat period of those magneto-Rossby waves synchronizes an underlying conventional α − Ω -dynamo by periodically changing either the field storage capacity in the tachocline or some portion of the α -effect therein. We also strengthen the argument that the Suess-de Vries cycle appears as an 193-year beat period between the 22.14-year Hale cycle and a spin-orbit coupling effect related with the 19.86-year rosette-like motion of the Sun around the barycenter. [ABSTRACT FROM AUTHOR]

We consider a conventional α – Ω -dynamo model with meridional circulation that exhibits typical features of the solar dynamo, including a Hale-cycle period of around 20 years and a reasonable shape of the butterfly diagram. With regard to recent ideas of a tidal synchronization of the solar cycle, we complement this model by an additional time-periodic α -term that is localized in the tachocline region. It is shown that amplitudes of some decimeters per second are sufficient for this α -term to become capable of entraining the underlying dynamo. We argue that such amplitudes of α may indeed be realistic, since velocities in the range of m s−1 are reachable, e.g., for tidally excited magneto–Rossby waves. [ABSTRACT FROM AUTHOR]