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.
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