Differential Geometry III (Summer 21) – Applications to Fluid Mechanics –

This is a BMS advanced course. The lecture will be held in English.

Contents

Many systems that arise in Fluid Physics can be interpreted as the motion of a Newtonian particle in an infinite dimensional Riemannian manifold, subject to certain potential or magnetic forces. Bringing in ideas from Riemannian geometry is helpful both for the mathematical understanding and in the context of algorithms for Fluid Simulation. Here are some examples of problems that we will discuss in detail:

• Incompressible fluid flow in a container M as a geodesics in the group of volume-preserving diffeomorphisms of M. (video: Bunny-Teapot collision).
• Bubble rings underwater. (Footage - Simulation side-by-side video)
• Magnetohydrostatics of Solar loops (one of our solar movies, I am not afraid of a conflict with the refereeing process).

The class should be accessible to anyone having some familiarity with differentiable manifolds.

Material

Additional Material:

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