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We prove analytic criteria for the existence of finite-time attracting and repelling material surfaces and lines in three-dimensional unsteady flows. The longest lived such structures define coherent structures in a Lagrangian sense. Our existence criteria involve the invariants of the velocity gradient tensor along fluid trajectories. An alternative(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)
[1] Application of recent geometric tools for Lagrangian coherent structures (LCS) shows that material attraction in geostrophic velocities derived from altimetry data imposed an important constraint to the motion of drifters from the Grand Lagrangian Deployment (GLAD) in the Gulf of Mexico. This material attraction is largely transparent to traditional(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)
Using precision measurements of tracer particle trajectories in a two-dimensional fluid flow producing chaotic mixing, we directly measure the time-dependent stretching field. This quantity, previously available only numerically, attains local maxima along lines that coincide with the stable and unstable manifolds of hyperbolic fixed points of Poincaré(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)
We use direct Lyapunov exponents (DLE) to identify Lagrangian coherent structures in two different three-dimensional flows, including a single isolated hairpin vortex, and a fully developed turbulent flow. These results are compared with commonly used Eulerian criteria for coherent vortices. We find that, despite additional computational cost, the DLE(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)