Volume Transport by a 3D Quasigeostrophic Heton

Oceanic flows self-organize into coherent vortices which strongly influence their transport and mixing properties. Counter-rotating vortex pairs can travel long distances and carry trapped fluid as they move. These structures are often modeled as hetons, viz. counter-rotating quasigeostrophic point vortex pairs with equal circulations. Here, we investigate the structure of the transport induced by a single three-dimensional heton. The transport is determined by the Hamiltonian structure of the velocity field induced by the heton's component vortices. The dynamics displays a sequence of bifurcations as one moves through the heton-induced velocity field in height. These bifurcations create and destroy unstable fixed points whose associated invariant manifolds bound the trapped volume. Heton configurations fall into three categories. Vertically aligned hetons do not move and do not transport fluid. Horizontally aligned hetons have a single parameter, the horizontal vortex half-separation $Y$, and simple scaling shows the dimensional trapped volume scales as $Y^3$. Tilted hetons are described by two parameters, $Y$ and the vertical vortex half-separation $Z$, rendering the scaling analysis more complex. A scaling theory is developed for the trapped volume of tilted hetons showing that it scales as $Z^4/Y$ for large $Z$. Numerical calculations illustrate the structure of the trapped volume and verify the scaling theory.