Resonance phenomena in a time-dependent, three-dimensional model of an idealized eddy.

We analyze the geometry of Lagrangian motion and material barriers in a time-dependent, three-dimensional, Ekman-driven, rotating cylinder flow, which serves as an idealization for an isolated oceanic eddy and other overturning cells with cylindrical geometry in the ocean and atmosphere. The flow is forced at the top through an oscillating upper lid, and the response depends on the frequency and amplitude of lid oscillations. In particular, the Lagrangian geometry changes near the resonant tori of the unforced flow, whose frequencies are rationally related to the forcing frequencies. Multi-scale analytical expansions are used to simplify the flow in the vicinity of resonant trajectories and to investigate the resonant flow geometries. The resonance condition and scaling can be motivated by simple physical argument. The theoretically predicted flow geometries near resonant trajectories have then been confirmed through numerical simulations in a phenomenological model and in a full solution of the Navier-Stokes equations.

Robust transport barriers resulting from strong Kolmogorov-Arnold-Moser stability.

Hamiltonian systems that locally violate the twist condition arise in many applications. Numerical simulations reveal that, when systems of this type are perturbed, the degenerate or nontwist tori are remarkably stable. This phenomenon, which we refer to as strong Kolmogorov-Arnold-Moser (KAM) stability, is shown to be linked to very small resonance widths near degenerate tori. Quantitative estimates of degenerate resonance widths are derived and bifurcations of degenerate resonances are described. Strong KAM stability leads to robust transport barriers, which are important in all of the many applications in which Hamilitonians with the nontwist property arise.

Persistent transport barrier on the West Florida Shelf.

Analysis of drifter trajectories in the Gulf of Mexico has revealed the existence of a region on the southern portion of the West Florida Shelf (WFS) that is not visited by drifters that are released outside of the region. This so-called "forbidden zone" (FZ) suggests the existence of a persistent cross-shelf transport barrier on the southern portion of the WFS. In this letter a year-long record of surface currents produced by a Hybrid-Coordinate Ocean Model simulation of the WFS is used to compute Lagrangian coherent structures (LCSs), which reveal the presence of a persistent cross-shelf transport barrier in approximately the same location as the boundary of the FZ. The location of the cross-shelf transport barrier undergoes a seasonal oscillation, being closer to the coast in the summer than in the winter. A month-long record of surface currents inferred from high-frequency (HF) radar measurements in a roughly 60 km × 80 km region on the WFS off Tampa Bay is also used to compute LCSs, and these also reveal the presence of transient transport barriers. While the HF-radar-derived transport barriers cannot be unambiguously linked to the boundary of the FZ, this analysis does demonstrate the feasibility of monitoring transport barriers on the WFS using a HF-radar-based measurement system. The implications of a persistent cross-shelf transport barrier on the WFS for the development of harmful algal blooms on the shoreward side of the barrier are considered.