Dynamo and Dynamics, a Mathematical Challenge

By: Pascal Chossat (Editor), Dieter Armbruster (Editor), Iuliana Oprea (Editor)

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Hardcover | 31 July 2001

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416 Pages

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24.13 x 16.51 x 3.18

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This book contains the lectures given at the workshop "Dynamo and dynamics, a mathematical challenge" held in Cargese from August 21 to 26, 2000. The workshop differed from most previous conferences on the dynamo effect in two important respects. First, it was at this international conference that the experimental observation of homogeneous fluid dynamos was first reported. Second, the conference gathered scientists from very different fields, thus showing that thepynamo problem has become an interdisciplinary subject involving not only astrophysicists and geophysicists, but also scientists working in dynamical systems theory, hydrodynamics, and numerical simulation, as well as several groups in experimental physics. This book thus reports important results on various dynamo studies in these different contexts: - Decades after the discovery of the first analytic examples of laminar fluid dynamos, the self-generation of a magnetic field by a flow ofliquid sodium has been reported by the Karlsruhe and Riga groups. Although there were no doubts concerning the self generation by the laminar Roberts-type or Ponomarenko-type flows that were used, these experiments have raised interesting questions about the influence of the turbulent fluctuations on the dynamo threshold and on the saturation level of the magnetic field.

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Preface
Participants
A nonstationary dynamo experiment in a braked torus	p. 1
Riga Dynamo Experiment	p. 9
Generation of magnetic field in the Couette-Taylor system	p. 17
Dynamo action, between numerical experiments and liquid sodium devices	p. 25
MHD in von Karman Swirling flows	p. 35
Dynamo action in a forced Taylor-Green vortex	p. 51
On the possibility of an homogeneous MHD dynamo in the laboratory	p. 59
Saturation of a Ponomarenko type fluid dynamo	p. 67
Dynamo Action due to Ekman layer Instability	p. 75
Hunting for dynamos: eight different liquid sodium flows	p. 83
Thermal flow in a rotating spherical gap with a dielectrophoretic central force field	p. 93
Preliminary Measurement of the Turbulent Magnetic Diffusivity in three dimensions	p. 101
Saturation mechanism in a model of the Karlsruhe dynamo	p. 109
Sheared helical turbulence and the helicity constraint in large-scale dynamos	p. 117
The inverse cascade in turbulent dynamos	p. 125
Rotating magnetoconvection in dependence on stratification, diffusive processes, and boundary conditions	p. 133
Small- and large-scale dynamo action in simple forced flows	p. 145
Convection driven dynamos in rotating spherical fluid shells	p. 153
Dynamos in rotating and nonrotating convection in the form of asymmetric squares	p. 163
Magnetoconvection	p. 173
On the application of grid-spectral method to the solution of geodynamo equations	p. 181
Super- and counter-rotating jets and vortices in strongly magnetic spherical Couette flow	p. 189
Large- and small-scale dynamo action	p. 199
Dynamo problems in spherical and nearly spherical geometries	p. 207
Anelastic planetary magnetohydrodynamics	p. 217
The Galactic Dynamo	p. 225
Turbulent Diamagnetism and Galactic Dynamo	p. 233
Parker instability with Coriolis force and magnetic reconnection as a part of the galactic fast dynamo action	p. 239
Magnetic helicity flux and the nonlinear galactic dynamo	p. 247
Helioseismic tests of dynamo models	p. 253
Asymptotic WKBJ-studies of solar dynamo waves: 1D and 2D cases	p. 261
Dynamo effect with inertial modes in a spherical shell?	p. 271
Two types of nonlinearities in magnetic dynamo	p. 279
The solar dynamo: axial symmetry and homogeneity broken	p. 289
Alpha-quenched [alpha][superscript 2][Omega] dynamo waves in stellar shells	p. 297
Two-dimensional disk dynamos with vertical outflows into a halo	p. 305
Structurally stable heteroclinic cycles and the dynamo dynamics	p. 313
Two-component dynamical model of the solar cycle	p. 323
Symmetries of the solar dynamo: comparing theory with observation	p. 331
Suicidal and parthenogenetic dynamos	p. 339
Heteroclinic cycles and fluid motions in rotating spheres	p. 347
Convection-driven dynamos, amplitude equations and large-scale fields	p. 355
A heteroclinic model of geodynamo reversals and excursions	p. 363
Aspects of the dynamics underlying solar and stellar dynamo models	p. 371
Modulation and symmetry-breaking in low-order models of the solar dynamo	p. 381
Table of Contents provided by Blackwell. All Rights Reserved.

Dynamo and Dynamics, a Mathematical Challenge

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Hardcover

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