Recent developments in the theory of instability by magnetic buoyancy are discussed in an astrophysical context and, where appropriate, extended to provide a more unified picture. Emphasis is placed on the effects of density stratification and rotation, which are usually stabilizing. In one stronglystratified and rapidly-rotating parameter r6gime, however~ it is possible to render a magnetic field configuration unstable by increasing the "statically-stable' stratification, although increasing it beyond a certain limit eventually stabilizes the system, as one would intuitively expect.We find that stratification exerts a strongly stabilizing influence in the solar radiative interior, despite the high thermal diffusivity K. Rotation plays a rather minor role. We emphasize the importance of a 'doubly-diffusive' parameter D e involving the ratio of K to rt, the magnetic diffusivity, and find that magnetic buoyancy instability typically requires field strengths in excess of about 50 000 G. The development time ties in with the rise-time of buoyant flux tubes in a stably-stratified environment calculated by Parker ( 1974Parker ( , 1975. A re aso nable gradient of molecular weight in the central core could only stabilize a (mainly) toroidal field strong enough to affect the neutrino flux if the magnetic diffusivity r/were rather smaller than is usually supposed, for otherwise such a field would be subject to either a doubly-diffusive magnetic instability, which would initially take the form of overstable buoyancy oscillations, or rapid ohmic decay.In the solar convection zone we find that the rotation of the Sun has an extremely strong and suppressing influence on magnetic buoyancy instability, and that this is only likely to occur for large field strengths of about 1000 G in the top half of the zone.

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This article reviews work on the dynamics of a rapidly rotating electrically conducting fluid in the presence of a corotating magnetic field. While the separate action of either rotation or a magnetic field produces strong dynamical constraints, their simultaneous action can result in comparatively weak net constraints and novel phenomena then arise. A systematic account of these phenomena is given and certain applications to natural systems (with emphasis on the dynamics of the Earth's liquid core) are outlined.

Reflexion coefficients greater than unity have now been predicted for a variety of different systems involving waves propagating towards a shear layer, but almost invariably only in regions of parameter space for which the layer exhibits Kelvin-Helmholtz instability. This paper contains a study of two examples in which, for appropriate parameter values, there are no such instabilities to obscure (or even prevent) the ‘over-reflexion’ of an incident wave, namely(a)hydro-magnetic internal gravity waves meeting a vortex-current sheet in a stratified fluid and(b)magneto-acoustic waves meeting a vortex sheet in a compressible fluid. In the former case the energetic aspects of over-reflexion are examined in detail, thus displaying the way in which the excess reflected energy is extracted from the mean motion and the sense in which the transmitted wave may be viewed, by analogy with certain concepts employed in plasma physics, as a carrier of so-called ‘negative energy’.