An Advanced Study Institute sponsored by NATO on “Magnetohydrodynamic Phenomena in Rotating Fluids” was held in Cambridge, England, from 26 June to 4 July 1972. The aim of the meeting was to provide, through invited lectures, a systematic account of those aspects of the geophysics of the earth's core and of astrophysics in which both rotation effects and magnetic effects play an important part. In addition to the invited lectures, shorter contributions and discussions were strongly encouraged. The main Sessions and the Session Chairmen were as follows:A The earth's magnetism and planetary magnetism magnetism Sir Edward BullardB Convection, differential rotation, and magneto-hydrodynamics in the sun Dr N. O. WeissC Stellar and interstellar magnetism; pulsars Prof. E. SpiegelD Boundary layers and detached shear layers and spin-up problems Prof. E. R. BentonE Waves and instabilities influenced by Lorentz and/or Coriolis forces Dr R. HideF Dynamo theory Prof. P. H. RobertsThese Chairmen, together with Professor P. A. Gilman and Dr H. K. Moffatt, who acted as Director of the Institute, constituted the Organising Committee. The summary of the meeting which follows has been substantially written by Dr Weiss (sessions B and C), Dr Hide (A and E), Professor Benton (D) and Professor Roberts (F), whose willing collaboration is gratefully acknowledged.There were just over a hundred participants, the great majority of whom were accommodated at Trinity College, Cambridge, for the duration of the meeting.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112073001928

Report on the NATO Advanced Study Institute on magnetohydrodynamic phenomena in rotating fluids

Many traditional ideas concerning the chemistry, the temperature, the distribution of heat sources, and the density of the lower mantle and core have recently been challenged. Some of this research has a direct bearing on the mechanism by which the earth's magnetic field is generated.

An interdisciplinary conference was held in Melbourne, Florida, on March 7–9 , 1972, to discuss these ideas. Our objective as specialists from the fields of seismology, geochemistry, paleomagnetism, astronomy, solidstate geophysics, and dynamo theory was to discuss the compatability of some of our own favored hypotheses about the earth's lower mantle and core with alternative hypotheses from other disciplines. Questions considered by the conference included the following:

International Conference on the Core-Mantle Interface

Die Grundideen der Magnetohydrodynamik der gemittelten Felder, wie sie von M. STEENBECK, K.-H. Radler und F. KRAUSE entwickelt wurden, werden auf Probleme der Warmeleitung in turbulenten fluiden Medien angewandt. Als Hauptergebnis wird gezeigt, das das Auftreten einer Dynamowirkung in einer homogenen isotropen spiegelsymmetrischen Turbulenz dem zweiten Hauptsatz der Thermodynamik widerspricht. Demgegenuber hat der nichtspiegelsymmetrische Anteil in einer solchen turbulenz keinen Einflus auf den Warmestrom. Ferner wird eine anisotrope Warmeleitfahigkeit fur den Fall nachgewiesen, das in dem Medium ein starkes Magnetfeld vorhanden ist. (Siehe auch Addendum, S. 87)



The basic ideas of the mean-fields magnetohydrodynamics developed by M. STEENBECK, K.-H. K.-H. Radler and F. KRAUSE are applied to heat conduction in turbulent fluids. As the main result it is shown that dynamo excitation caused by homogeneous isotropic mirror-symmetric turbulence contradicts the second principle law of thermodynamics, whereas the non-mirrorsymmetric part of that turbulence does not influence the heat flow. Furthermore an anisotropic heat conductivity is calculated for the case that there is a strong magnetic field. (See also Addendum, p. 87)

Heat flow and magnetic field diffusion in turbulent fluids

Using Kraichnan's direct interaction approximation in the induction equations we set up the kinematic equations governing behavior of an ensemble average magnetic field under homogeneous, incompressible, mirror symmetric isotropic velocity turbulence. We demonstrate that the normal modes of the field depend on the solutions to a nonlinear single integral equation. For a simple form of the velocity turbulence we have investigated some of the properties of the integral equation. In particular, we have been able to construct a particular solution. We also point out what remains to be done if we are to obtain all the modes of the ensemble average magnetic field. We have done this calculation so that the behaviour and normal modes of the field can be investigated at arbitrary magnetic Reynolds' numbers. This is in contrast to customary approximations (like first‐order smoothing theory) which normally are valid only for very small Reynolds numbers, if at all, and which therefore omit large regimes of considerable physical interest.

Application of Kraichnan's direct interaction approximation to kinematic dynamo theory. I. Incompressible isotropic turbulence and a singular integral equation

Mean-field magnetohydrodynamics or focused on the kinematic side of the problem, mean-field electrodynamics is a theory that has turned out t o be useful for the investigation of various problems of magnetohydrodynamic turbulence. I t is a theory of the large-scale fields in turbulent conducting fluids where the large-scale effects of the small-scale fields are regarded as certain averages of products of correlated small-scale quantities. The dynamo theory of cosmic magnetic fields has proved t o be an important field of application for this theory. As a first example, we note Larmor’s suggestion’ that magnetic fields of celestial bodies might be maintained by self-excited dynamos. Cowling,’ who utilized this idea, tried t o explain the magnetic fields of sunspots by a dynamo mechanism. His result, although negative, is now the well-known Cowling’s theorem: dynamo excitation does not exist for fields of simple pattern, for example, axisymmetric fields. Thus, it is clear from the start that dynamo excitation, if it exists, will provide fields of a more complicated structure. Moreover, when magnetic fields are observed, there are complicated velocity fields, which oftcn appear as convective motions. This is true for sunspots, which have their origin in the convection zone, and for the Earth’ s magnetic field, the origin of which would then have t o be assumed in the Earth’s core. The idea that convective motions might provide the necessary complicated pattern was first expressed by Frenke13 in connection with the Earth’s magnetic field and by Gurewitch and Lebedinskii4 in relation t o sunspots. Estimations of the order of magnitude, indeed, do not contradict this idea. Thus, turbulent motions have become of interest for the dynamo problem. However, one is reminded here of the intriguing argument by Cowling’ that it is difficult t o believe that a completely disordered, chaotic turbulence can provide a magnetic field with large-scale structure. This doubt, obviously, results from knowledge of the second principal law of thermodynamics.

The present status of mean field magnetohydrodynamics and the turbulent dynamo problem.

Regenerative kinematic-dynamo action under incompressible isotropic velocity turbulence, noting turbulent Lorentz force role

I. Lerche

Papers

Kinematic-dynamo action under incompressible, isotropic velocity turbulence.