Welcome to the Vortex Dynamics Research Group. We are one of the Applied Mathematics groups in the Institute of Mathematics at the University of St Andrews in Scotland.

We are studying a wide range of complex, nonlinear fluid phenomena that generically occur in extremely high Reynolds number (essentially inviscid) flows, prime examples being the Earth's atmosphere and oceans, other planetary atmospheres (and oceans just in case!), and the magnetised solar interior. Many of the problems that we deal with involve stably-stratified flows (dense fluid lying under less dense fluid), as well as rotating flows (e.g. such as arises from the Earth's rotation). We employ a variety of techniques, including mathematical analysis (asymptotic approximations, deriving simplified equations, finding exact and approximate solutions, obtaining rigorous bounds, examining the stability of equilibria, etc...) and innovative, fast, accurate numerical methods (e.g. Lagrangian "contour-based" methods, hybrid algorithms, etc...). The Lagrangian methods, originating in contour dynamics and contour surgery (Dritschel, J. Comput. Phys. 77, 240-266, 1988), have been extended to apply to many physical systems from 2D Euler to 3D non-hydrostatic, including magnetohydrodynamics. For a review of these "contour advection" methods, see (Fontane and Dritschel, J. Comput. Phys. 228, 6411-6425, 2009), and for the latest "Combined Lagrangian Advection Method" (CLAM), see (Dritschel and Fontane, J. Comput. Phys. 229, 5408-5417, 2009). Please contact David Dritschel if you would like to use any of these codes.

There is a significant collaboration with applied centres dedicated to atmosphere and ocean dynamics worldwide, including the UK Meteorological Office, the European Centre for Medium-Range Weather Forecasts, Southhampton Oceanography Centre, the Universities of Reading, London and Cambridge, as well as many European, North American and Australian centres.