The dynamics of the solar tachocline (Astrophysical and Geophysical Fluid Dynamics)

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.

keywords: applied mathematics, astrophysics, MHD, fluid dynamics, waves

Astrophysical and Geophysical Fluid Dynamics
The group in Leeds is one of the leading groups in the field of Astrophysical and Geophysical Fluid Dynamics, with international reputation in dynamo theory, astrophysical MHD and convection. The strength of the group is recognised by the award of several prizes and special fellowships. The group also holds one of the largest grants ever awarded to the University of Leeds. The nine permanent members of staff work with eighteen postdocs and postgraduate students.

The group is actively engaged in research in a wide-range of areas of astrophysical and geophysical fluid dynamics: from planetary dynamics (the geodynamo and planetary dynamos) through solar, stellar and galactic dynamics to highly compressible and relativistic dynamics on the largest scales. Magnetic fields are a strong theme, and the group is interested in how planets (like the Earth), stars (like the Sun), neutron stars, black holes and galaxies generate their magnetic fields through dynamo action. On the Sun, the well-known eleven-year sunspot cycle is a manifestation of the solar dynamo; indeed the solar magnetic field underlies all solar magnetic phenomena such as solar flares, coronal mass ejections and the solar wind. In the Earth, magnetic fields are generated by convection in the molten iron core, and it has recently become possible to solve the fundamental equations that govern the motion of fluids and the generation of magnetic fields, and successfully reproduce many of the observed features of the geomagnetic field. At the other end of the scale, magnetic fields are implicated in the formation of spectacular jets coming from neutron stars, black holes and galaxies. Without magnetic fields, the group has interests in waves and hydrodynamic instabilities in rotating stratified fluids, with applications to the Earth's atmosphere and ocean (and with application to other planets).