Mathematical Modelling of Ocean Tides (Astrophysical and Geophysical Fluid Dynamics)

Tides are the oceanic response to well-known gravitational forcing by the Sun and Moon. These hugely energetic oscillations influence various parts of the Earth system, such as the history of the lunar orbit, the transport of heat by the large-scale ocean circulation, and the rate of advance of ice sheets flowing into the polar oceans.

Although the physics of tidal flows is thought to be well understood, mathematical and numerical modelling of ocean tides remains a challenge. This is due to the complex nature of the coastline and ocean floor, and the rather sensitive dependence of tidal amplitudes to local resonances and dissipative processes. This PhD project would focus on one or more aspects of ocean tides, each requiring appropriate solution of linear or nonlinear partial differential equations. Possible topics are (i) using Laplace's tidal equations to derive simple mathematical models of changes in tidal regimes since the last Ice Age, a period over which sea-levels have risen by over 100m; (ii) developing novel numerical methods for computational models of tides on regional or global scales; (iii) developing models of how long ocean waves are modified by gravitational self-attraction and depression of the underlying elastic Earth; (iv) mathematical analysis and numerical modelling of `internal tidal waves', which are almost invisible from the ocean surface. The results will have widespread implications throughout the earth and ocean sciences.

The research 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 magneto-hydrodynamics 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 a wide range of research in astrophysical and geophysical fluid dynamics. 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. 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 indeed with application to other planets).

keywords: fluid dynamics, ocean, atmosphere, numerical modelling, mathematical modelling, waves, applied mathematics