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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)
Recent developments in identifying Lagrangian coherent structures from finite time velocity data have provided a theoretical basis for understanding chaotic transport in general flows with aperiodic dependence on time. As these theoretical developments are extended and applied to more complex flows, an accurate and general numerical method for computing(More)
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)
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)
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)
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)
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)