Nonlinear astrophysical dynamos - The solar cycle as a nonlinear oscillation of the general magnetic field driven by the nonlinear dynamo and the associated modulation of the differential-rotation-global-convection system

Abstract

An attempt is made to examine the nonlinear reaction of a magnetic field with field-generating fluid motions in a dynamo as a possible mechanism for limiting the growing amplitude of the 22-yr solar cycle. Attention is given to formulation of the dynamo equation, the nonlinear dynamo equation, a local analysis of the nonlinear dynamo equation, and nonlinear dynamo-wave oscillations. The cases of a shallow and a deep upper zone are considered, and the response of the nonlinear dynamo system to temporary cessation of global-convection processes is investigated. Direct evidence that a nonlinear dynamo system is currently operating in the solar convection zone is discussed. It is concluded that magnetic oscillations of the solar cycle can be understood as nonlinear dynamo-wave oscillations driven by differential rotation and solar convection, which in turn are modulated by the reaction of the magnetic field in association with the solar cycle.