Analytical and Numerical Investigations of Linear and Nonlinear Magnetohydrodynamic Wave Propagation

This thesis contains investigations on four relatively independent, magnetohydrodynamic (MHD) wave problems and their relevance to astrophysical processes. The introduction to these four wave problems is outlined in Chapter 1. In Chapter 2, the damping of the Alfven mode in stochastic astrophysical fluids is considered. The properties of coherent small-amplitude Alfven waves propagating along a strong mean background magnetic field in a turbulent plasma is investigated by applying the projection operator technique. Unlike earlier work, the background turbulence is assumed to be time-dependent, homogeneous and axisymmetric. The coherent Alfven mode is shown to be damped, and the damping decrement is estimated for cases of relevance to MHD wave propagation in the solar corona. In Chapter 3, numerical simulation of two-dimensional, unsteady, ideal MHD equations by the method of characteristics is presented. The numerical scheme is described in detail and the numerical results are compared with analytic solutions. The nonlinear results for MHD waves in a magnetic flux tube are analyzed. The results show that the method of characteristics can be successfully applied to solve the ideal MHD equations. In Chapter 4, we study two-dimensional, global, nonlinear MHD waves of large scales in a zonal magnetic field on the surface of a rotating sphere. We obtain two kinds of finite-amplitude MHD waves propagating in the azimuthal direction relative to the uniformly rotating atmosphere. One of the waves is an inertial wave of the Rossby-Haurwitz type, modified by the presence of zonal magnetic field, while the other is a magnetic Alfven-like wave which is modified by the uniform rotation; these results generalize earlier work on the purely hydrodynamical problem to include magnetic field effects. In Chapter 5, we investigate standing MHD wave modes for a perfectly conducting but viscid magnetofluid in a gravitationally stratified magnetic flux tube. We obtain numerical results for three series of modes in an isothermal flux tube: Alfvenic, quasi-fast, and quasi-slow. The quasi-slow mode series is novel, having been missed previously. We illustrate the physical nature of the three MHD eigenmode series using three approximate, characteristic dispersion relations. The relevance of this problem to umbral oscillations in sunspots is discussed.