Geometric Hydrodynamics

Record

Yes

Abstract

This course consists of two parts.

In the first part I introduce the geometric approach to fluid mechanics. This approach is based on description of fluid as a Hamiltonian mechanics on the manifold of the group of diffeomorphisms (Arnold,1966). I further discuss a spacetime covariant approach developed by Lichnerowitz (1941) and Carter (1979) and variational approach to (Hamilton principle) fluid mechanics.

In the second part I address applications of geometric approach to conservation laws and introduce a notion of anomalies.

Anomalies were initially discovered in quantum field theories in late 1960s. They soon became a foundational principle of quantum field theory. Very recent development has revealed that, quit remarkably, the anomalies of quantum field theory are integral part of fluid dynamics.

The course intended for graduate students and researchers with a background in mathematical physics and interest in geometry.