Geometry of cross-stream mixing in a double-gyre ocean model

New dynamical systems techniques are used to analyze fluid particle paths i n an eddy resolving, barotropic ocean model of the Gulf Stream. Specificall y, the existence of finite-time invariant manifolds associated with transie nt, mesoscale events such as ring detachment and merger is proved based on computer-assisted analytic results. These "Lagrangian" invariant manifolds completely organize the dynamics and mark the pathways by which fluid parce ls may be exchanged across stream. In this way, the Lagrangian flow geometr y of a detaching ring or a ring-jet interaction event, as well as the exact associated particle flux, is obtained. The detaching ring geometry indicates that a significant amount of the flui d entrained by the ring originates in a long thin region on the far side of the jet and that this region extends as far upstream as the western bounda ry current. In the ring-stream interaction case, particle transport occurs both to and from the ring and is concentrated in thin regions on the near s ide of the jet and around the perimeter of the ring.