In strongly stratified geophysical fluids such as the stratosphere and the ocean, the
vertical mixing of tracers is largely due to patches of turbulence that are intermittent
in time and space. Heuristic models for this type of mixing are studied which
extend that of Dewan (1981a). The recognition that, in these models, fluid particles
undergo continuous-time random walks allows the derivation of closed-form results
for the particle-position statistics. The particle dispersion is shown generally to be
diffusive in the long-time limit. However, the early-time, non-diffusive regime is also
analysed, since a time-scale estimate indicates its practical importance, in particular
for stratospheric mixing.
Because the restratification of fluid patches previously homogenized by turbulence
takes a finite time, the probability for a fluid region to become turbulent may depend
on the time elapsed since it has last been turbulent. This introduces a ‘memory
effect’ whose consequences for the tracer mixing are analysed in detail using a simple
non-Markovian model.
The heuristic models studied allow the large-scale dispersive effects of the turbulent
patches to be inferred from the properties of individual patches. This highlights those
properties that might most usefully be determined from investigations of the dynamics
of the turbulent patches themselves.