The first diagnostic is a modification to the Nakamura effective diffusivity. Calculations on patches of the ocean of size 10 degrees by 10 degrees using this diagnostic highlight the role of topography and of wave-mean flow interactions in determining the mixing structure.
The second diagnostic, the Lyapunov Diffusivity, combines the tracer-based effective diffusivity with the particle-based Lyapunov exponent. Application to consider isentropic mixing in the upper troposphere/lower stratosphere shows there to be significant longitudinal variation to the strength of mixing at the Northern subtropical jet, with the strongest barrier over Asia and the Western Pacific, a weaker barrier over the Western Atlantic, and mixing regions at the jet exits over the Eastern Pacific and Atlantic. Again, the role of wave-mean flow interactions in determining this mixing structure will be highlighted.
There is scope for both diagnostics to be applied to a range of atmospheric and oceanic problems where the velocity field is known or can be estimated and a measure of eddy diffusivity is required.