Seminar Computational and Applied Mathematics

Abstract:
Some time ago, Milo Viviani and myself unveiled numerical simulations of incompressible 2-D hydrodynamics on the sphere indicating a connection between the long-time behavior of 2-D Euler equations and integrability conditions for "blob dynamics". After presenting these results, I was asked an insightful question:

The phase space underlying the model in the simulations is compact. Because the dynamics in the model is also Hamiltonian, we have Poincaré recurrence. But the dynamics in the simulations, leading to blob formations, seem contractive. Isn't the mechanism for blob formations instead induced by fictitious dissipation, introduced via the numerical time-discretization?

I didn’t have a good answer at the time, but the question stayed with me. Today I have an answer, which is the subject of this talk.