Multiscaling in passive scalar advection as stochastic shape dynamics

Details Multiscaling in passive scalar advection as stochastic shape dynamics Multiscaling in passive scalar advection as stochastic shape dynamics

1997-11-05

arxiv.org/abs/cond-mat/9711034v1

Physics

Condensed Matter

Statistical Mechanics

14 pages, LaTeX

Scientific paper

10.1103/PhysRevE.57.5511

The Kraichnan rapid advection model is recast as the stochastic dynamics of tracer trajectories. This framework replaces the random fields with a small set of stochastic ordinary differential equations. Multiscaling of correlation functions arises naturally as a consequence of the geometry described by the evolution of N trajectories. Scaling exponents and scaling structures are interpreted as excited states of the evolution operator. The trajectories become nearly deterministic in high dimensions allowing for perturbation theory in this limit. We calculate perturbatively the anomalous exponent of the third and fourth order correlation functions. The fourth order result agrees with previous calculations.

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