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We introduce a Lagrangian definition for the boundaries of coherent structures in two-dimensional turbulence. The boundaries are defined as material lines that are linearly stable or unstable for longer times than any of their neighbors. Such material lines are responsible for stretching and folding in the mixing of passive tracers. We derive an analytic… (More)

The motion of inertial (i.e., finite-size) particles is analyzed in a three-dimensional unsteady simulation of Hurricane Isabel. As established recently, the long-term dynamics of inertial particles in a fluid is governed by a reduced-order inertial equation, obtained as a small perturbation of passive fluid advection on a globally attracting slow manifold… (More)

- Francois Lekien, Chad Coulliette, Arthur J Mariano, Edward H Ryan, Lynn K Shay, George Haller +1 other
- 2005

High-resolution ocean velocity data has become readily available since the introduction of very high frequency (VHF) radar technology. The vast amount of data generated so far, however, remains largely unused in environmental prediction. In this paper, we use VHF data of the Florida coastline to locate Lagrangian coherent structures (LCS) hidden in ocean… (More)

- Jerrold E Marsden, Shane D Ross, Michael Dellnitz, Frederic Gabern, Katalin Grubits, Oliver Junge +25 others
- 2005

To Henri Poincaré on the 150th anniversary of his birth. Abstract. The title of this paper is inspired by the work of Poincaré [1890, 1892], who introduced many key dynamical systems methods during his research on celestial mechanics and especially the three body problem. Since then, many researchers have contributed to his legacy by developing and applying… (More)

High-frequency (HF) radar technology produces detailed velocity maps near the surface of estuaries and bays. The use of velocity data in environmental prediction, nonetheless, remains unexplored. In this paper, we uncover a striking flow structure in coastal radar observations of Monterey Bay, along the California coastline. This complex structure governs… (More)

- Andrew C Poje, George Haller, Igor Mezi
- 1999

The relationship between the statistical and geometric properties of particle motion in aperiodic, two-dimensional ows is examined. Finite-time invariant manifolds associated with transient hyperbolic trajectories are shown to divide the ow into distinct regions with similar statistical behavior. In particular, numerical simulations of simple, eddy… (More)

- Thomas Peacock, George Haller
- 2013

I n April 2010, fine, airborne ash from a volcanic eruption in Iceland caused chaos throughout European airspace. The same month, the explosion at the Deepwater Horizon drilling rig in the Gulf of Mexico left a gushing oil well on the sea floor that caused the largest offshore oil spill in US history. A year later the Tohoku tsunami hit the coast of Japan,… (More)

- Francisco J Beron-Vera, Yan Wang, María J Olascoaga, Gustavo J Goni, George Haller, F J Beron-Vera +1 other
- 2013

abstract 2 Mesoscale oceanic eddies are routinely detected from instantaneous velocities derived 3 from satellite altimetry data. While simple to implement, this approach often gives 4 spurious results and hides true material transport. Here it is shown how geodesic 5 transport theory, a recently developed technique from nonlinear dynamical systems, 6… (More)

The asymptotic dynamics of finite-size particles is governed by a slow manifold that is globally attracting for sufficiently small Stokes numbers. For neutrally buoyant particles ͑suspensions͒, the slow dynamics coincide with that of infinitesimally small particles, therefore the suspension dynamics should synchronize with Lagrangian particle motions.… (More)