The Geometry of Fluid Dynamics

Tudor Ratiu (EPFL & Shanghai Jiao Tong University - Switzerland and China)

21-Jan-2022, 16:00-17:00 (2 years ago)

Abstract: Fluid motion has a remarkable geometric structure generated by Poisson structures on the Hamiltonian and variational structures on the Lagrangian side. I will briefly review the standard results for ideal incompressible homogeneous flows and then show how this is extended to fluids with advected quantities. A much more elaborate extension happens for the Eringen model of liquid crystals because these fluids have internal structure. Then I will introduce a momentum map with values in differential characters that captures topological information, something the classical momentum map cannot do. This has consequences in hydrodynamics, specifically for Clebsch variables, since it permits to deal with solutions whose helicity is integer valued.

geometric topology

Audience: researchers in the topic


GEOTOP-A seminar

Series comments: Web-seminar series on Applications of Geometry and Topology

Organizers: Alicia Dickenstein, José-Carlos Gómez-Larrañaga, Kathryn Hess, Neza Mramor-Kosta, Renzo Ricca*, De Witt L. Sumners
*contact for this listing

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