Small-scale mixing, large-scale advection, and stratospheric tracer distributions

The vertical mixing of tracers in the stratosphere is mainly due to patches of three-dimensional turbulence. which are highly intermittent in time and space. A simple heuristic model of this form of mixing is developed and employed to examine the effect of small-scale mixing on passive stratospheric tracers. The model is based on random-walk ideas, and it leads to an analog of the usual advection-diffusion equation in which the diffusion operator is replaced by a convolution operator taking the intermittency of the mixing into account. In its simplest form, this operator is defined by two parameters: these are estimated from midlatitude lower-stratospheric balloon data using a stochastic model of turbulent patches. The behavior of tracer distributions in some idealized flows shows how intermittency makes mixing less effective in damping the small-scale tracer fluctuations that arise through differential advection. This has consequences for stratospheric tracer distributions, which are demonstrated using numerical simulations based on observed stratospheric winds. Specifically, the new model of mixing leads to a horizontal tracer spectrum that is shallower, and closer to a k e power law, than the spectrum obtained with a diffusive parameterization of mixing. The horizontal scale below which intermittent mixing differs significantly from diffusion is estimated to be 15 km or so: remarkably, this coincides with the dissipative scale below which dissipation by small-scale mixing is crucial for tracer evolution.