Statistically accurate simulations for atmospheric flows
(2009) 12th Seminar “NUMDIFF” on Numerical Solution of Differential and Differential-Algebraic Equations — Location: Halle, Germany (14.September.2009)
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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. (2009). Statistically accurate simulations for atmospheric flows. 12th Seminar “NUMDIFF” on Numerical Solution of Differential and Differential-Algebraic Equations, Halle, Germany. https://hdl.handle.net/2078.5/158500