Analytic calculation of anomalous scaling in random shell models for a passive scalar

Details Analytic calculation of anomalous scaling in random shell models for a passive scalar Analytic calculation of anomalous scaling in random shell models for a passive scalar

1997-02-07

arxiv.org/abs/chao-dyn/9702005v2

Nonlinear Sciences

Chaotic Dynamics

3 pages, 1 figure, revised version

Scientific paper

10.1103/PhysRevLett.78.4926

An exact non-perturbative calculation of the fourth-order anomalous correction to the scaling behaviour of a random shell-model for passive scalars is presented. Importance of ultraviolet (UV) and infrared (IR) boundary conditions on the inertial scaling properties are determined. We find that anomalous behaviour is given by the null-space of the inertial operator and we prove strong UV and IR independence of the anomalous exponent. A limiting case where diffusive behaviour can influence inertial properties is also presented.

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