This advanced course will give an introduction to vortex dynamics aimed at applied mathematicians. Only a basic knowledge of fluid dynamics will be assumed. Mathematical prerequisites are a knowledge of calculus, vector calculus and complex analysis.

Take a look at a review article on "Point vortex motion" that will appear in the upcoming "Encyclopedia of Mathematical Physics". It provides an accessible introduction to the key ideas underlying vortex dynamics.

Some of the topics to be covered:

• concept of vorticity; the Biot-Savart integral
• point vortex dynamics; the Hamiltonian formulation; vortex collapse, leap-frogging
• vortex motion around topography (Kirchhoff-Routh theory)
• the vortex patch model; Kirchhoff ellipse; Moore-Saffman-Kida generalizations
• theory of vortex interactions (the "elliptical vortex model");
• vortex merger
• vortex stability
• contour dynamics; numerical methods