Dynamo theory for the interface between the convection zone and the radiative interior of a star: Part I model equations and exact solutions
作者:
EdwardE. Deluca,
PeterA. Gilman,
期刊:
Geophysical & Astrophysical Fluid Dynamics
(Taylor Available online 1986)
卷期:
Volume 37,
issue 1-2
页码: 85-127
ISSN:0309-1929
年代: 1986
DOI:10.1080/03091928608210092
出版商: Taylor & Francis Group
关键词: Dynamo processes;magnetohydrodynamics;nonlinear dynamics;rotating fluids;solar magnetism;stellar magnetism
数据来源: Taylor
摘要:
In this paper we derive a set of equations which model magnetic field generation and maintenance in a thin region, (∼ 104)km thick, below the solar convection zone, and present some simple exact solutions. Energy to drive the dynamo is assumed to come from helical convection that overshoots into this region. Differential rotation and meridional circulation result only from feedbacks by the induced fields. The equations are derived for a homogeneous incompressible fluid in Cartesian geometry. The momentum equation, magnetic induction equation, and the continuity equation are included in the analysis. We assume velocity and magnetic field patterns have an aspect ratio of ∼1/10 (radial to horizontal scale), that the large scale velocities are smaller than the convection zone velocities, a few meters per sec, and the large scale magnetic fields are of the order of 104Gauss. Finally we assume that the time scale of interest is the advective time scale. Using these assumptions, we derive governing equations in which the Coriolis force balances the Lorentz force, the pressure gradient force, and the viscosity, and in which the magnetic fields are maintained by the α effect but significantly modified by the above velocity fields. The results of this model will be discussed in following papers.
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