Hydrodynamic and Magnetohydrodynamic Stability (AGFD)
A recurring theme in many different areas of fluid dynamics is the transition to more and more complicated flows as the system is forced increasingly hard. Hydrodynamic stability theory seeks to understand the nature of these transitions, both in terms of the underlying fluid dynamics, as well as more abstractly, in terms of the symmetries that are broken by the various bifurcations. Applications include a variety of geophysically and astrophysically motivated problems, as well as many aspects of classical fluid dynamics, such as the flow between differentially rotating cylinders,both with and without magnetic fields. The PhD project would involve studying one of these applications, and numerically investigating the resulting instabilities.
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).
This project is eligible for School of Mathematics Doctoral Training Grant funding - please contact us for more information.