Enduring Lagrangian coherence of a Loop Current ring assessed using independent observations.

Ocean flows are routinely inferred from low-resolution satellite altimetry measurements of sea surface height assuming a geostrophic balance. Recent nonlinear dynamical systems techniques have revealed that surface currents derived from altimetry can support mesoscale eddies with material boundaries that do not filament for many months, thereby representing effective transport mechanisms. However, the long-range Lagrangian coherence assessed for mesoscale eddy boundaries detected from altimetry is constrained by the impossibility of current altimeters to resolve ageostrophic submesoscale motions. These may act to prevent Lagrangian coherence from manifesting in the rigorous form described by the nonlinear dynamical systems theories. Here we use a combination of satellite ocean color and surface drifter trajectory data, rarely available simultaneously over an extended period of time, to provide observational evidence for the enduring Lagrangian coherence of a Loop Current ring detected from altimetry. We also seek indications of this behavior in the flow produced by a data-assimilative system which demonstrated ability to reproduce observed relative dispersion statistics down into the marginally submesoscale range. However, the simulated flow, total surface and subsurface or subsampled emulating altimetry, is not found to support the long-lasting Lagrangian coherence that characterizes the observed ring. This highlights the importance of the Lagrangian metrics produced by the nonlinear dynamical systems tools employed here in assessing model performance.

Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean.

Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here, we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent Lagrangian eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived Sargassum distributions.

Forecasting sudden changes in environmental pollution patterns.

The lack of reliable forecasts for the spread of oceanic and atmospheric contamination hinders the effective protection of the ecosystem, society, and the economy from the fallouts of environmental disasters. The consequences can be dire, as evidenced by the Deepwater Horizon oil spill in the Gulf of Mexico in 2010. We present a methodology to predict major short-term changes in environmental contamination patterns, such as oil spills in the ocean and ash clouds in the atmosphere. Our approach is based on new mathematical results on the objective (frame-independent) identification of key material surfaces that drive tracer mixing in unsteady, finite-time flow data. Some of these material surfaces, known as Lagrangian coherent structures (LCSs), turn out to admit highly attracting cores that lead to inevitable material instabilities even under future uncertainties or unexpected perturbations to the observed flow. These LCS cores have the potential to forecast imminent shape changes in the contamination pattern, even before the instability builds up and brings large masses of water or air into motion. Exploiting this potential, the LCS-core analysis developed here provides a model-independent forecasting scheme that relies only on already observed or validated flow velocities at the time the prediction is made. We use this methodology to obtain high-precision forecasts of two major instabilities that occurred in the shape of the Deepwater Horizon oil spill. This is achieved using simulated surface currents preceding the prediction times and assuming that the oil behaves as a passive tracer.

Invariant-tori-like Lagrangian coherent structures in geophysical flows.

The term "Lagrangian coherent structure" (LCS) is normally used to describe numerically detected structures whose properties are similar to those of stable and unstable manifolds of hyperbolic trajectories. The latter structures are invariant curves, i.e., material curves of fluid that serve as transport barriers. In this paper we use the term LCS to describe a different type of structure whose properties are similar to those of invariant tori in certain classes of two-dimensional incompressible flows. Like stable and unstable manifolds, invariant tori are invariant curves that serve as transport barriers. There are many differences, however, between traditional LCSs and invariant-tori-like LCSs. These differences are discussed with an emphasis on numerical techniques that can be used to identify invariant-tori-like LCSs. Structures of this type are often present in geophysical flows where zonal jets are present. A prime example of an invariant-torus-like LCS is the transport barrier near the core of the polar night jet in the Earth's lower and middle stratospheres in the austral winter and early spring; this is the barrier that traps ozone-depleted air inside the ozone hole. This example is investigated using both a simple analytically prescribed flow and a velocity field produced by a general circulation model of the Earth's atmosphere.