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Courses in Mathematics and Statistics Level 1 Modules Level 2 Modules Level 3 Modules Level 4 Modules Level 5 Modules Honours timetable 2011/2012 Sem. 1 2011/2012 Sem. 2 2012/2013 Sem. 1 & Sem. 2 2013/2014 Sem. 1 & Sem. 2

MT5809 ADVANCED FLUID DYNAMICS This is a 24 lecture course which follows on from MT4509 Aims This course will examine current research in fluid dynamics, with a particular focus on meteorology and oceanography. The large-scale atmosphere and oceans behave quite unlike a 'classical' fluid owing to the presence of stable density stratification and rotation. As a result, the fluid motion is dominated by slow, 'vortical' or eddying motions (like cyclones) which generally spin slower than the Earth. Superposed on this slow motion are relatively fast wave-like motions analogous to surface waves on a pond. These lectures describe the mathematical basis of these fundamentally different types of motion, and furthermore illustrate the increasingly important role of computer modelling in this research. Objectives - Review the mathematical properties of vorticity, including the concept of 'inversion' (obtaining the velocity field from vorticity), and vortex dynamics (stretching, tilting and baroclinic generation). - Individually consider the effects of rotation and stable stratification, then their joint effect on fluid motion. - Introduce 'potential vorticity' and explore its properties. - Examine the approximate separation of the fluid motion into slow/fast or 'balanced/imbalanced' motions. - Consider the role of computation in current research, and illustrate several applications to geophysical turbulence, vortex interactions, and wave-vortex interactions. Assessment 100% by two-and-a-half hour examination Prerequisites MT4509 (Fluid Dynamics) Availability Every year in semester 1 at 11 Lecturer Dr J N Reinaud Click here for access to past examination papers for this module. Click here to see the University Course Catalogue entry. Revised: JOC (September 2010)