Quantifying asymmetric wave breaking and two-way transport

Effective diffusivity calculated from a scalar field that obeys the advection-diffusion equation has proved useful for estimating the permeability of unsteady boundaries of air masses such as the edge of the stratospheric polar vortex and the extratropical tropopause. However, the method does not discriminate the direction of transport-whereas some material crosses the boundary from one side to the other, some material does so in the other direction-yet the extant method concerns only the net transport. In this paper, the diagnostic is extended to allow partitioning of fluxes of mass and tracer into opposing directions. This is accomplished by discriminating the regions of "inward" and "outward" wave breaking with the local curvature of the tracer field. The utility of the new method is demonstrated for nonlinear Kelvin-Helmholtz instability and Rossby wave breaking in the stratosphere using a numerically generated tracer. The method successfully quantifies two-way transport and hence the direction of wave breaking - the predominantly equatorward breaking of Rossby waves in the extratropical middle stratosphere, for example. Isolated episodes of mixing are identified well, particularly by the mass flux that primarily arises from the tracer filaments. Comparison of different transport schemes suggests that the results are reasonably robust under a varying subgrid representation of the model.