Chapter 9 - Dynamo Theory

@inproceedings{Gilbert2003Chapter9,
  title={Chapter 9 - Dynamo Theory},
  author={Andrew D. Gilbert},
  year={2003}
}
Short Timescale Core Dynamics: Theory and Observations
Fluid motions in the Earth’s core produce changes in the geomagnetic field (secular variation) and are also an important ingredient in the planet’s rotational dynamics. In this article we review
Decay and Amplification of Magnetic Fields
This chapter presents a series of very simple flows that can, or cannot, act as dynamos. The journey begins with magnetic field decay by Ohmic dissipation in the absence of flows, followed by
Weakly nonlinear analysis of the  α effect
We address mathematical issues raised by the so-called  α effect of dynamo theory, which is a dynamo mechanism arising in conducting flows with small scale fluctuations. Analytical results on the  α
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We study the dynamo threshold of a helical flow made of a mean plus a fluctuating part. Two flow geometries are studied: (i) solid body and (ii) smooth. Two well-known resonant dynamo conditions,
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Steady, pressure-driven incompressible laminar flow of an electrically conducting fluid down a helically symmetric pipe is known to be capable of sustaining a dynamo at a fairly low hydrodynamic
Fast and furious dynamo action in the anisotropic dynamo
Abstract In the limit of large magnetic Reynolds numbers, it is shown that a smooth differential rotation can lead to fast dynamo action, provided that the electrical conductivity or magnetic
Turbulent 2.5-dimensional dynamos
We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components $(u(x,y,t),v(x,y,t),w(x,y,t))$ that is sometimes referred to as a 2.5-dimensional (2.5-D)
The mean electromotive force generated by elliptic instability
Abstract The mean electromotive force (EMF) associated with exponentially growing perturbations of an Euler flow with elliptic streamlines in a rotating frame of reference is studied. We are
Wellposedness of Linearized Taylor Equations in Magnetohydrodynamics
This paper is a first step in the study of the so-called Taylor model, introduced by J.B. Taylor in Taylor, Proc R Soc A 274(1357):274–283, 1963. This system of nonlinear PDE’s is derived from the
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