# Chaotic Lagrangian models for turbulent relative dispersion

## TL;DR

This paper introduces a deterministic chaotic model for turbulent relative dispersion that avoids common stochastic simulation drawbacks, accurately analyzes dispersion statistics, and demonstrates efficiency across various Reynolds numbers.

## Contribution

The paper presents a novel chaotic Lagrangian model for turbulence that removes the sweeping effect and accurately captures dispersion statistics using FSLE analysis.

## Key findings

- Chaotic flows effectively model turbulent trajectories.
- Model removes the sweeping effect via quasi-Lagrangian coordinates.
- Numerical experiments show model efficiency across Reynolds numbers.

## Abstract

A deterministic multi-scale dynamical system is introduced and discussed as prototype model for relative dispersion in stationary, homogeneous and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian Chaos. The anomalous "sweeping effect", a known drawback common to kinematic simulations, is removed thanks to the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model are accurately analysed by computing the Finite-Scale Lyapunov Exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous and isotropic conditions. The mathematics of the model is relatively simple and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer and/or boundary layer turbulence models as well as Lagrangian predictability studies.