Chaotic Lagrangian models for turbulent relative dispersion

A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relativedispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, heretrajectory transport and mixing properties are entirely controlled by Lagrangian chaos. The anomalous “sweepingeffect,” a known drawback common to kinematic simulations, is removed through the use of quasi-Lagrangiancoordinates. Lagrangian dispersion statistics of the model are accurately analyzed by computing the finite-scaleLyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scalingexponents provide a severe test to decide whether model simulations are in agreement with theoretical expectationsand/or observation. The results of our numerical experiments cover a wide range of “Reynolds numbers” and showthat chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectoriesin stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, ina geophysical context, potential applications may regard small-scale parametrization issues in general circulationmodels, mixed layer, and/or boundary layer turbulence models as well as Lagrangian predictability studies