The Dynamics of the Solar Tacholine

The most exciting observational discovery in solar physics in recent years is that of the tachocline, a thin, convectively stable region of strong velocity shear located between the convective and radiative zones. Although thin, this region is believed to play a crucial role in the evolution and dynamics of the solar interior. This project will explore the dynamics of the tachocline -- both its wave motions and possible instabilities -- through a study of what are known as the "shallow water" magnetohydrodynamic equations. These equations, which are extremely interesting mathematically, are the astrophysical counterpart to the standard hydrodynamic shallow water equations often employed in atmospheric studies, extended so as to include the effects of a magnetic field.