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It is widely accepted that astrophysical magnetic fields are generated by dynamo action. In many cases, these fields exhibit organisation on a scale larger than that of the underlying turbulent flow (e.g. the 11-year solar cycle). The mechanism for the generation of so-called large-scale fields remains an open problem. In cases where the magnetic Reynolds number (Rm) is small, dynamo-generated fields are coherent but at (the astrophysically relevant) high Rm, the fields are overwhelmed by small-scale fluctuating field. Recently Tobias and Cattaneo have shown that an imposed large-scale shear flow can suppress the small-scale fluctuations and allow the large-scale temporal behaviour to emerge. Shear is also believed to modify the electromotive force by introducing correlations between the flow and the field. However, in previous models at high Rm the shear is often artificially imposed or driven by an arbitrary body force. Here we consider a simple kinematic model of a convective dynamo in which shear is self-consistently driven by the presence of a horizontal temperature gradient (resulting in a thermal wind) and a rotation vector that is oblique to gravity. By considering a -dimensional system, we are able to reach high Rm so that the dynamo approaches the asymptotic regime where the growth rate becomes approximately independent of Rm. We find the flows studied here to be excellent small-scale dynamos, but with very little systematic behaviour evident at large Rm. We attribute this to being unable to self-consistently generate flows with both large (net) helicity and strong shear in this setup. [ABSTRACT FROM AUTHOR]

Waves in a thin layer on a rotating sphere are studied. The effect of a toroidal magnetic field is considered, using the shallow water ideal MHD equations. The work is motivated by suggestions that there is a stably stratified layer below the Earth’s core mantle boundary, and the existence of stable layers in stellar tachoclines. With an azimuthal background field known as the Malkus field,,being the co-latitude, a non-diffusive instability is found with azimuthal wavenumber. A necessary condition for instability is that the Alfvén speed exceedswhereis the rotation rate andthe sphere radius. Magneto-inertial gravity waves propagating westward and eastward occur, and become equatorially trapped when the field is strong. Magneto-Kelvin waves propagate eastward at low field strength, but a new westward propagating Kelvin wave is found when the field is strong. Fast magnetic Rossby waves travel westward, whilst the slow magnetic Rossby waves generally travel eastward, except for somemodes at large field strength. An exceptional very slow westwardmagnetic Rossby wave mode occurs at all field strengths. The current-driven instability occurs forwhen the slow and fast magnetic Rossby waves interact. With strong field the magnetic Rossby waves become trapped at the pole. An asymptotic analysis giving the wave speed and wave form in terms of elementary functions is possible both in polar trapped and equatorially trapped cases. [ABSTRACT FROM PUBLISHER]

In this article we examine the range of applicability of the anelastic approximation, which is often used in describing the dynamics of geophysical and astrophysical flows. Specifically, we consider two linear problems: magnetoconvection and magnetic buoyancy, and compare the fully compressible solutions with those determined by solving the anelastic problem. We further compare a subsequent simplification introduced by Lantz [Dynamical behavior of magnetic fields in a stratified, convecting fluid layer. Ph.D. Thesis, Cornell University: Ithaca, U.S.A., 1992] with the anelastic formulation. We find that for the magnetoconvection problem the anelastic approximation works well if the departure from adiabaticity is small (as expected) and determine where the approximation breaks down. The results for magnetic buoyancy are less straightforward, with the accuracy of the approximation being determined by the growth rate of the instability. We argue that these results make it difficult to assess a priori whether the anelastic approximation will provide an accurate approximation to the fully compressible system for stably stratified problems. Thus, unlike the magnetoconvection problem, for magnetic buoyancy it is difficult to provide general rules as to when the anelastic approximation can be used. [ABSTRACT FROM AUTHOR]