Vertical dispersion of Lagrangian tracers in fully developed stably stratified turbulence

Abstract

We study the effect of different forcing functions and of the local gradient Richardson number Rig on the vertical transport 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 differ from the homogeneous and isotropic case. Moreover, the model gives insight into the mixture of linear and nonlinear physics in the problem, as well as on the different processes responsible for vertical turbulent dispersion.