New dynamical systems techniques are used to analyze fluid particle paths in an eddy resolving, barotropic ocean model of the Gulf Stream. Specifically, the dynamic Lagrangian structures associated with transient mesoscale events such as ring detachment and merger are constructed.
Under a set of explicit conditions, the presence of a saddle type stagnation point in the Eulerian velocity field leads to the the existence of a hyperbolic trajectory in the Lagrangian flow.
The Lagrangian invariant manifolds associated with such a trajectory completely organize the dynamics and mark the pathways by which fluid parcels may be exchanged across stream. In this way, the geometry and particle fluxes associated with a detaching ring and a ring--jet interaction event are studied.

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