Date
Mon, 13 Jun 2022
Time
15:30 - 16:30
Location
L3
Speaker
JAMES-MICHAEL LEAHY
Organisation
Imperial College London

Noether’s theorem plays a fundamental role in modern physics by relating symmetries of a Lagrangian to conserved quantities of the Euler-Lagrange equations. In ideal fluid dynamics, the theorem relates the particle labeling symmetry to a Kelvin circulation law. Circulation is conserved for incompressible flows and, otherwise, is generated by advected variables through the momentum map due to a broken symmetry. We will introduce variational principles for fluid dynamics that constrain advection to be the sum of a smooth and geometric rough-in-time vector field. The corresponding rough Euler-Poincare equations satisfy a Kelvin circulation theorem and lead to a natural framework to develop parsimonious non-Markovian parameterizations of subgrid-scale dynamics.

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