1996/05/31 by A. Wirth, L. Biferale · 1 citation
Physics and Astronomy · #chao-dyn #nlin.CD
paper · pdf · doi:10.1103/physreve.54.4982
Plain LaTex, 15 pages, 4 figure available upon request to [email protected]
arxiv created 1996/05/31 · arxiv updated 2009/11/30
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 ∝ km-ξ, where km 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 ξ= 2/3 the anomalous scaling exponents ζp 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.