Magnetohydrodynamic Waves in a Gravitationally Stratified Fluid

Waves and oscillations are ubiquitous in the Sun. Magnetohydrodynamic (MHD) waves
in a gravitationally stratified medium are of fundamental importance in understanding
the physical phenomena observed in the solar atmosphere. Waves may be generated by
turbulent motion in the solar convection zone. Magnetic fields of varying scales permeate
the atmosphere of the Sun; these may provide a channel for MHD waves to propagate into
the solar atmosphere.
The theory of MHD waves in a stratified medium has been well developed, although it
is far from complete. In this thesis we aim to contribute to the development of this theory.
The work in this thesis can be broadly divided into two sections. The first of these concerns
the role of buoyancy when MHD waves propagate within a gravitational field. Secondly,
we study the global resonance of waves in a stratified atmosphere. We primarily employ
analytical methods to make progress.
We study buoyancy-driven MHD waves with more depth and rigour than previous
studies. We begin with a magnetic field that is parallel to gravity. We give a clearer picture
of the situation, which has previously been misinterpreted. We generalise previous work
to include a more complex and realistic background including temperature variation and
partial ionisation. We also briefly consider a magnetic field perpendicular to gravity.
It has been shown that vertically propagating acoustic waves in a stratified atmosphere
may be trapped by a varying acoustic cut-off frequency. This trapping leads to a global
resonance in the entire solar atmosphere. We generalise previous work by including e.g.
non-vertical wave propagation, buoyancy and a magnetic field. We conclude that the
global resonance is a rather robust phenomenon and so may be an important mechanism in
supplying energy into the higher solar atmosphere.