Vertical dispersion of Lagrangian tracers in fully developed stably stratified turbulence

TL;DR

This paper investigates vertical dispersion of tracers in stratified turbulence, introducing a combined wave and random walk model that aligns well with numerical simulations, revealing the interplay of linear and non-linear processes.

Contribution

It presents a novel combined wave and random walk model for vertical dispersion in stratified turbulence, incorporating effects of local Richardson number and turbulence forcing.

Findings

Model agrees with direct numerical simulations

Vertical dispersion differs from isotropic turbulence

Insights into linear and non-linear physics interactions

Abstract

We study the effect of different forcing functions and of the local gradient Richardson number Rig on the vertical mixing of Lagrangian tracers in stably stratified turbulence under the Boussinesq approximation, and present a wave and continuous-time random walk model for single- and two- particle vertical dispersion. The model consists of a random superposition of linear waves with their amplitude based on the observed Lagrangian spectrum of vertical velocity, and a random walk process to capture overturning that depends on the statistics of Rig among other Eulerian quantities. The model is in good agreement with direct numerical simulations of stratified turbulence, where single- and two-particle dispersion differs from the homogeneous and isotropic case. Moreover, the model gives insight into the mixture of linear and non-linear physics in the problem, as well as on the different processes responsible for vertical turbulent dispersion.