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We consider a general class of statistical mechanical models of coherent structures in turbulence, which includes models of two-dimensional fluid motion, quasi-geostrophic flows, and dispersive waves. First, large deviation principles are proved for the canonical ensemble and the microcanonical ensemble. For each ensemble the set of equilibrium macrostates… (More)

- B Turkington, A Majda, K Haven, M DiBattista
- Proceedings of the National Academy of Sciences…
- 2001

An equilibrium statistical theory of coherent structures is applied to midlatitude bands in the northern and southern hemispheres of Jupiter. The theory imposes energy and circulation constraints on the large-scale motion and uses a prior distribution on potential vorticity fluctuations to parameterize the small-scale turbulent eddies. Nonlinearly stable… (More)

Many situations in complex systems require quantitative estimates of the lack of information in one probability distribution relative to another. In short term climate and weather prediction, examples of these issues might involve the lack of information in the historical climate record compared with an ensemble prediction, or the lack of information in a… (More)

Here, Kaplan-Yorke type maps are utilized as simplified models to assess new strategies for quantifying predictability through information theory. These models gives rise to a wide variety of “climate” distributions from nearly Gaussian to highly non-Gaussian. For complex models, it is almost impossible to compute proposed theoretical measures of… (More)

Statistical equilibrium lattice models of coherent structures in geostrophic turbulence, formulated by discretizing the governing Hamiltonian continuum dynamics, are analyzed. The first set of results concern large deviation principles (LDP's) for a spatially coarse-grained process with respect to either the canonical and/or the microcanonical formulation… (More)

We consider a general class of statistical mechanical models of coherent structures in turbulence, which includes models of two-dimensional fluid motion, quasigeostrophic flows, and dispersive waves. First, large deviation principles are proved for the canonical ensemble and the microcanonical ensemble. For each ensemble the set of equilibrium macrostates… (More)

The large deviation principle is proved for a class of L2-valued processes that arise from the coarse-graining of a random field. Coarse-grained processes of this kind form the basis of the analysis of local mean-field models in statistical mechanics by exploiting the long-range nature of the interaction function defining such models. In particular, the… (More)

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