Statistical Mechanics of Hamiltonian Particle Mesh method
(2008) Workshop on geometric and stochastic methods in geophysical fluid dynamics — Location: Bremen, Germany (7.January.2008)
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- Abstract
- A Hamiltonian particle-mesh method for quasi-geostrophic potential vorticity flow is proposed. The microscopic vorticity field at any time is an area- and energy-conserving rearrangement of the initial field. We construct a statistical mechanics theory to explain the long-time behavior of the numerical solution. The statistical theory correctly predicts the spatial distribution of particles as a function of their point vorticity. A nonlinear relation between the coarse grained mean stream function and mean vorticity fields is predicted, consistent with the preservation of higher moments of potential vorticity reported in [R. V. Abramov, A. J. Majda 2003, PNAS 100 3841–3846].
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Dubinkina, S., & Frank, J. (2008). Statistical Mechanics of Hamiltonian Particle Mesh method. Workshop on geometric and stochastic methods in geophysical fluid dynamics, Bremen, Germany. https://hdl.handle.net/2078.5/158545