Chapter 9 - Dynamo Theory

  title={Chapter 9 - Dynamo Theory},
  author={Andrew D. Gilbert},
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
Parametric instability of the helical dynamo
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,
Nonlinear dynamos in laminar, helical pipe flow
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


of the geomagnetic field in terms of fluid motions in the outermost cor e has been revived and new methods of data analysis have been applied to this problem. Second, physically more realistic models
The earth's dynamo
Abstract Recent developments in geodynamo theory have advanced along two distinct tracks. On the one hand, a mean field approach is adopted. With reasonable assumptions about the nature of the α- and
Lectures on solar and planetary dynamos
Introduction 1. Fundamentals of dynamo theory P. H. Roberts 2. Solar and stellar dynamics N. O. Weiss 3. Convection and magnetoconvection in a rapidly rotating sphere M. R. E. Proctor 4. Solar
Nonlinear Restrictions on Dynamo Action
Astrophysical dynamos operate in the limit of small magnetic diffusivity. In order for magnetic reconnection to occur, very small magnetic structures must form so that diffusion becomes effective.
Fast Dynamo Theory
Basic ideas of dynamo theory are reviewed, the emphasis being on kinematic induction in the limit of infinite magnetic Reynolds number. The distinction between a dynamo in a perfect conductor, and
The Galactic Dynamo
The purpose of this paper is to present a model of Galactic dynamo driven by supernova explosions. I first describe, in physical and mathematical terms, the threefold impact of supernova-driven
Origin of Magnetic Fields in Astrophysics (Turbulent "Dynamo" Mechanisms)
We consider the generation of magnetic fields under astrophysical conditions. Principal attention is paid to "dynamo" mechanisms, i.e., mechanisms in which the energy of the magnetic field is drawn
A convection-driven dynamo I. The weak field case
  • A. Soward
  • Physics
    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1974
A hydromagnetic dynamo model is considered. A Boussinesq, electrically conducting fluid is confined between two horizontal planes and is heated from below. The system rotates rapidly about the
Homogeneous dynamos and terrestrial magnetism
  • E. Bullard, H. Gellman
  • Physics
    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1954
The main object of the paper is to discuss the possibility of a body of homogeneous fluid acting as a self-exciting dynamo. The discussion is for the most part confined to the solution of Maxwell’s
Solar-cycle dynamo wave propagation
Dynamo waves, as solutions of the dynamo equations governing the solar cycle, propagate along isorotation surfaces inside the Sun. This theorem, universal in most dynamo models of the solar cycle, is