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Oceanic flows self-organize into coherent vortices which strongly influencetheir transport and mixing properties. Counter-rotating vortex pairs can travellong distances and carry trapped fluid as they move. These structures are oftenmodeled as hetons, viz. counter-rotating quasigeostrophic point vortex pairswith equal circulations. Here, we investigate the structure of the transportinduced by a single three-dimensional heton. The transport is determined by theHamiltonian structure of the velocity field induced by the heton's componentvortices. The dynamics displays a sequence of bifurcations as one moves throughthe heton-induced velocity field in height. These bifurcations create anddestroy unstable fixed points whose associated invariant manifolds bound thetrapped volume. Heton configurations fall into three categories. Verticallyaligned hetons do not move and do not transport fluid. Horizontally alignedhetons have a single parameter, the horizontal vortex half-separation $Y$, andsimple scaling shows the dimensional trapped volume scales as $Y^3$. Tiltedhetons are described by two parameters, $Y$ and the vertical vortexhalf-separation $Z$, rendering the scaling analysis more complex. A scalingtheory is developed for the trapped volume of tilted hetons showing that itscales as $Z^4/Y$ for large $Z$. Numerical calculations illustrate thestructure of the trapped volume and verify the scaling theory.

Volume Transport by a 3D Quasigeostrophic Heton