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More than half a century ago, Bullard suggested that the Earth's dynamo might be driven by the motions created in the Earth's core by the luni-solar precession. The precessionally forced motion of the mantle drives core flow through viscous forces and also, because of the electrical conductivity of the deep mantle, through magnetic forces. Both these couplings are thought to be insignificant in comparison with the topographical coupling created by the oblateness of the core-mantle interface. Because of technical difficulties in studying dynamo action in nonspherical bodies of electrically conducting fluid, this is the first serious attempt to study dynamo action by topographically forced flows. It describes the novel numerical methods that were employed, the tests that were devised to validate these methods, and the successful outcome of those tests. Some preliminary results for these dynamos are presented. It is shown that, in some parameter ranges, the magnetic field produced by the dynamos enhances the vigor of the precessional motions.

Contrary to the usual belief that MHD intermediate shocks are extraneous, we have recently shown by numerical solutions of dissipative MHD equations that intermediate shocks are admissible and can be formed through nonlinear wave steepening from continuous waves. In this paper, the formation, structure and stability of intermediate shocks in dissipative MHD are considered in detail. The differences between the conventional theory and ours are pointed out and clarified. We show that all four types of intermediate shocks can be formed from smooth waves. We also show that there are free parameters in the structure of the intermediate shocks, and that these parameters are related to the shock stability. In addition, we show that a rotational discontinuity can not exist with finite width, indicate how this is related to the existence of time‐dependent intermediate shocks, and show why the conventional theory is not a good approximation to dissipative MHD solutions whenever there is rotation in magnetic field.

Contrary to the usual belief that MHD intermediate shocks are extraneous, we show in this paper by numerical solutions of resistive MHD equations that at least some of the intermediate shocks are admissible and can be formed through nonlinear steepening from a continuous wave. The result is of importance not only to the MHD shock theory but also to studies such as magnetic field reconnection models.

We present a two‐dimensional, force‐balanced magnetic field model in which flux tubes have constant pVγ throughout an extended region of the nightside plasma sheet, between approximately 36 RE geocentric distance and the region of the inner edge of the plasma sheet. We have thus demonstrated the theoretical existence of a steady state magnetic field configuration that is force‐balanced and also consistent with slow, lossless, adiabatic, earthward convection within the limit of the ideal MHD (isotropic pressure, perfect conductivity). The numerical solution was constructed for a two‐dimensional magnetosphere with a rectangular magnetopause and nonflaring tail. The primary characteristics of our steady state convection solution are (1) a pressure maximum just tailward of the inner edge of the plasma sheet and (2) a deep, broad minimum in equatorial magnetic field strength Bze, also just tailward of the inner edge. Our results are consistent with Erickson's (1985) convection time sequences, which exhibited analogous pressure peaks and Bze minima. Observations do not indicate the existence of a Bze minimum, on the average. We suggest that the configurations with such deep minima in Bze may be tearing‐mode unstable, thus leading to substorm onset in the inner plasma sheet.

A detailed numerical analysis has been conducted of the instability described by Finn and Kaw in which parallel currents in neighboring islands tend to coalesce into larger units. The existence of this coalescence instability in the ideal magnetohydrodynamic limit is confirmed, but no evidence is found for a threshold in island width. The linear growth rates are found to be rapid compared with those for purely resistive processes, and the linear mode structure has only a weak dependence on resistivity. In the nonlinear regime, saturation of the mode in the ideal case is observed due to flux piling up at the X point, while in the nonideal case the merging process is observed to proceed to completetion.

A simplified set of equations is derived that approximates the magnetohydrodynamic (MHD) Navier–Stokes equations for weakly nonlinear disturbances whose speeds are close to the MHD intermediate speed. Its shock structure solutions are then examined. The fast and slow shock solutions are uniquely specified by their Rankine–Hugoniot relations. However, the intermediate shock solutions, which are not unique, are characterized by the integral through the shock of the noncoplanar component of the magnetic field. For situations in which this integral is conserved, the Riemann problem is well defined and predicts the evolution of intermediate shocks. This analysis is substantiated by numerical computations.