Two-Dimensional Mixing, Edge Formation, and Permeability Diagnosed in an Area Coordinate

Two-dimensional mixing of a tracer is diagnosed using A, the area between the tracer contour and a reference contour, as the horizontal coordinate. In the absence of sources or sinks, the tracer distribution in the area coordinate is governed bywhereis the square of the equivalent length of the tracer contour and k is the constant microscale diffusion coefficient. While diffusion is necessary to invoke transport, the large-scale kinematics regulate the evolution of q through the stretching and redistribution of Le2. It is argued that Le2 is a useful, easy to compute diagnostic for irreversible transport, especially for identifying a barrier. Typical behaviors of Le2 in various flow regimes are illustrated using the numerically simulated Kelvin-Helmholtz billow. Signature of mixing is found in the irreversible growth of Le2, but the precise time dependence is complex due to interplay between advection and diffusion. Formation of the edges (concentrated gradients) and their permeability to mass are addressed using a kinematic model with prescribed Le2. Relevance of this model to the stratospheric polar vortex, midlatitude tropopause, and oceanic thermocline is discussed.