Direct numerical simulations of three-dimensional magnetohydrodynamic turbulence with kinetic and magnetic Reynolds numbers up to 100 are presented. Spatially intermittent magnetic fields are observed in a flow with nonhelical driving. Small-scale helical driving produces strong large-scale nearly force-free magnetic fields.

Helical and Nonhelical Turbulent Dynamos

As a consequence of the smallness of the electronic fine structure constant, the characteristic time scale for the free diffusive decay of a magnetic field in a planetary core is much less than the age of the Solar System, but the characteristic time scale for thermal diffusion is greater than the age of the Solar System. Consequently, primordial fields and permanent magnetism are small and the only means of providing a substantial planetary magnetic field is the dynamo process. This requires a large region which is fluid, electrically conducting and maintained in a non-uniform motion that includes a substantial RMS vertical component. The attributes of fluidity and conductivity are readily provided in the deep interiors of all planets and most satellites, either in the form of an Fe alloy with a low eutectic temperature (e.g. Fe-S-O in terrestrial bodies and satellites) or by the occupation of conduction states in fluid hydrogen or 'ice' (H2O-NH3-CH4) in giant planets. It is argued that planetary dynamos are almost certainly maintained by convection (compositional and/or thermal).

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Planetary magnetic fields

The time-scale of the variation in the length of the day is comparable to, or shorter than, the electromagnetic decay time, τη, of the mantle. This suggests that an electromagnetic theory for the origin of these fluctuations should not only depend on the electromechanical coupling time, τI, introduced by ROCHESTER (1960), but also on τη. It is shown that, when τI is small compared with τη, the fluctuation time for perturbations in the angular velocity of the mantle is of order τc=τI2/3τη1/3, and not τη. The possibility that τI is not large compared with τη for the case of the Earth is considered. Also, by means of a simple shellular model of the core, the role of Alfven waves in modifying the coupling of core to mantle is discussed. The relationship of this theory with that of BRAGINSKII (1970) is briefly noted. A new account is given of mantle induction which, although only valid at small magnetic Reynolds numbers (based on the conductivity of the mantle), is sufficiently general to permit the coupling of the mantle to an arbitrary slow motion on the core surface to be treated.

Electromagnetic Core-Mantle Coupling

If a conducting fluid shell is undergoing spin-axisymmetric differential rotation and overlies the dynamo generating region of a planet then it is capable of greatly reducing the non-spin-axisymmetric components of the generated field, provided the appropriate magnetic Reynolds number is large. The model, closely related to the electromagnetic skin effect, is quantified and applied to Saturn. The observed small dipole tilt (~1°) of Saturn's magnetic field can be explained because of the presence of a stably stratified conducting layer overlying the dynamo region. This layer is a predicted consequence of the thermal evolution, arises because of the limited solubility of helium in metallic hydrogen (Stevenson, 1980), and appears to be required by the Voyager infrared observations indicating depletion of helium from Saturn's atmosphere. The much larger dipole tilt angles of Jupiter and the Earth indicate the absence of any such stable, differentially rotating layer with a large magnetic Reynolds number.

Reducing the non-axisymmetry of a planetary dynamo and an application to saturn

Harvesting energy from automobile brake in contact and non-contact mode by conjunction of triboelectrication and electrostatic-induction processes

This paper describes an experimental and theoretical investigation of induction in a rotating conductor surrounded by a rigid conductor of finite or infinite extent. The results are applied to a discussion of induction in rotating eddies in the fluid core of the earth as a possible origin of the geomagnetic non-dipole field. Model experiments were made with rigid rotators in a steady magnetic field; the induced magnetic field was measured outside the conductors. The results confirmed the appropriate parts of the theoretical work. In the theoretical work solutions are first obtained for a rotator embedded in a solid conductor of infinite extent; a method is then developed for extending this solution to a finite surrounding conductor. Charts are given for the induced field on the surface of the earth due to a hypothetical rotator in the earth’s core. The analysis is based on integral solutions of the field equations; wherever possible the field vectors themselves are used rather than a vector potential. The induced magnetic fields depend on the relative symmetry of the rotator, the surrounding conductor, and the applied magnetic field. For an applied field parallel to the axis of rotation, the induced field is proportional to the angular velocity; for an applied field perpendicular to the axis, the induced field reaches a limit at high angular velocities. If both the surrounding conductor and the applied magnetic field have rotational symmetry about the axis there is no induced field outside the surrounding conductor. The conclusion of the geophysical discussion is that eddies must have radii of several hundred kilometres if they are to account for the observed magnitude of the non-dipole field. Because of the skin effect such large radii would not be tenable if the core material were effectively rigid. However, fluid motions must occur due to the electromagnetic forces, and the consequent magneto-hydrodynamic disturbances probably have decay lengths much larger than the rigid conductor skin depth; therefore arguments based on the rigid conductor skin depth are not applicable. Thus the eddy model might be satisfactory if the fluid motion does not seriously alter the basic induction mechanism.

F. J. Lowes

Papers

Electromagnetic induction in rotating conductors