Statistically preserved structures in shell models of passive scalar advection

Yoram Cohen, Thomas Gilbert, and Itamar Procaccia
Phys. Rev. E 65, 026314 – Published 25 January 2002
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Abstract

It was conjectured recently that statiscally preserved structures underlie the statistical physics of turbulent transport processes. We analyze here in detail the time-dependent (noncompact) linear operator that governs the dynamics of correlation functions in the case of shell models of passive scalar advection. The problem is generic in the sense that the driving velocity field is neither Gaussian nor δ correlated in time. We show how to naturally discuss the dynamics in terms of an effective compact operator that displays “zero modes,” which determine the anomalous scaling of the correlation functions. Since shell models have neither a Lagrangian structure nor “shape dynamics,” this example differs significantly from standard passive scalar advection. Nevertheless, with the necessary modifications, the generality and efficacy of the concept of statistically preserved structures are further exemplified. In passing we point out a bonus of the present approach, in providing analytic predictions for the time-dependent correlation functions in decaying turbulent transport.

  • Received 24 July 2001

DOI:https://doi.org/10.1103/PhysRevE.65.026314

©2002 American Physical Society

Authors & Affiliations

Yoram Cohen, Thomas Gilbert, and Itamar Procaccia

  • Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel

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Vol. 65, Iss. 2 — February 2002

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