A Synchronized Two-Dimensional $\alpha $–$\Omega $ Model of the Solar Dynamo
M. Klevs, Frank Stefani, L. Jouve
Abstract
Abstract We consider a conventional $\alpha $ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> – $\Omega $ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Ω</mml:mi> </mml:math> -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 $\alpha $ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -term that is localized in the tachocline region. It is shown that amplitudes of some decimeters per second are sufficient for this $\alpha $ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -term to become capable of entraining the underlying dynamo. We argue that such amplitudes of $\alpha $ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> may indeed be realistic, since velocities in the range of m s −1 are reachable, e.g., for tidally excited magneto–Rossby waves.