Anisotropic surface waves and instabilities under a vertical electromagnetic force

This thesis describes theoretical and experimental research into the anisotropic waves and instabilities which can be produced at the surface of a conducting fluid, or at the interface between a conducting and non-conducting fluid, when the conductor is subject to a vertical electromagnetic force due to the imposition of a horizontal magnetic field and an electric current. The basic theory of M.H.D.anisotropic surface waves is expanded to include the effect of surface tension, viscosity, and a two-fluid interface. Polar plots of phase and group velocity and lines of constant phase are presented for sets of experimentally feasible parameters. The nature of the anisotropy is discussed.' The problems of reflection and refraction, the initial impulse problem and the 'ship-wave' and 'fish-line' problems, as applied to anisotropic surface waves, are solved using methods of 'wave-crest kinematics. The requirements of a rig to demonstrate the anisotropic waves in the laboratory are discussed. Two different rigs are described. One using mercury produces inconclusive results. The other using electrolyte covered by organic solvents clearly demonstrates the existence of anisotropic waves, giving qualitative agreement with the theoretical predictions. As background to the theoretical study of the H.H.D.Rayleigh-Tayl,or instability, the influence of j x B forces on free surface shapes is examined. Variants of the instability itself are analysed, and it appears that some interesting instability motions may exist. The variation of orientation of the instability with the electromagnetic parameters is determined. Experiments and experimental techniques to demonstrate some of the predicted instabilities are described. A novel, large amplitude 'bridge' instability is recorded, and excellent agreement with theory is obtained in an orientation experiment