  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.
