Anomalous scaling in random shell models for passive scalars

Details Anomalous scaling in random shell models for passive scalars Anomalous scaling in random shell models for passive scalars

1996-05-31

arxiv.org/abs/chao-dyn/9605015v1

Nonlinear Sciences

Chaotic Dynamics

Plain LaTex, 15 pages, 4 figure available upon request to wirth@obs-nice.fr

Scientific paper

10.1103/PhysRevE.54.4982

A shell-model version of Kraichnan's (1994 {\it Phys. Rev. Lett. \bf 72}, 1016) passive scalar problem is introduced which is inspired from the model of Jensen, Paladin and Vulpiani (1992 {\it Phys. Rev. A\bf 45}, 7214). As in the original problem, the prescribed random velocity field is Gaussian, delta-correlated in time and has a power-law spectrum $\propto k_m^{-\xi}$, where $k_m$ is the wavenumber. Deterministic differential equations for second and fourth-order moments are obtained and then solved numerically. The second-order structure function of the passive scalar has normal scaling, while the fourth-order structure function has anomalous scaling. For $\xi = 2/3$ the anomalous scaling exponents $\zeta_p$ are determined for structure functions up to $p=16$ by Monte Carlo simulations of the random shell model, using a stochastic differential equation scheme, validated by comparison with the results obtained for the second and fourth-order structure functions.

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