Effects of transport barriers on global mixing and fluxes

The role of transport barriers, identified with local minima in effective diffusivity, is examined in terms of the decay rate of the global tracer variance and of the fluxes through the barriers. With an idealized 1D model, it is shown that the global variance of a passive tracer in a finite insulated domain decays exponentially if effective diffusivity is steady or temporally periodic. The decay rate depends sensitively on the magnitude of the minimum diffusivity. Since the tracer gradients are often greatest at the minimum diffusivity, the diffusive flux of the gravest mode does not necessarily minimize at the barrier; in fact, it is more likely to maximize there. When the strength of the barrier fluctuates, the time-averaged structure of the mode is similar to that of the time independent eigenmode, but the asymptotic decay rate diminishes due to a reduced correlation between the flux and gradient. These findings are confirmed with the results of 2D advection-diffusion calculations driven by the Met Office assimilated winds on isentropic surfaces in the upper troposphere and lower stratosphere.

For a given effective diffusivity profile, the flux profiles vary significantly with initial and boundary conditions of the tracer as well as the presence of forcing. With fixed boundary values of tracer, the flux is constant through the barrier, whereas when the tracer is relaxed to a profile with nonzero gradient, the flux becomes minimum at the barrier. It must be emphasized therefore that, while a minimal effective diffusivity is a useful measure of transport barrier, it is not a sole determinant of long-term net molecular transport across the barrier regions.