Tuesday 29 Apr 2014: CliMathNet e-seminar: Hamilton's Principle for the GFD Model Hierarchy
Prof Darryl Holm - Imperial College London
Harrison 209 15:00-16:00
Applying asymptotics, averaging and reduction by symmetry in Hamilton's principle for the Euler fluid equations governing a rotating, stratified incompressible flow produces the main sequence of GFD approximations. Each model in this sequence of approximations possesses a Kelvin circulation theorem, and conserves energy and potential vorticity (PV). Legendre transforming the symmetry-reduced Lagrangian yields the Lie-Poisson Hamiltonian formulation of GFD and its Eulerian conservation laws, which may be used to classify steady solutions as relative equilibria and determine sufficient conditions for their nonlinear stability.