F. Lekien, C. Coulliette, A.J. Mariano, E.H. Ryan, L.K. Shay, G. Haller, J.E. Marsden, Pollution Release Tied to Invariant Manifolds: A case Study for the Coast of Florida, Physica D, 210(1-2), pp 1--20, 2005.     Cited by: 6    Visited by: 3428

 

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Version 3.0. Re-Submitted to Physica D on June 14th, 2005. Size Format Viewer Figures 1 Mb 350 kb PDF 1.3 color 133 Mb 536 kb Postscript color

 

Animations

Screenshot Description Codec Reconstructed velocity field near Fort Lauderdale, Florida. The currents are obtained from two Very High Frequency radar/antenna located in Hollywood Beach, FL and in John Loyd Ntl Park (Fort Lauderdale, FL). See Shay et al., 2002 for details on the installation. Cinepak (Radius) 281 Mb Two parcels (black and white) integrated using the radar data, tricubic interpolation and a 4th order Runge-Kutta-Feldberg algorithm. The two parcels are released almost at the same position but their outcome is very different. The white parcels leaves the domain quickly; the black parcel recirculates near the coast. Cinepak (Radius) 21 Mb 22 Mb Direct Lyapunov exponent field based on the radar data. The domain is divided by a red Lagrangian structure. The structure is almost Lagrangian but not completely (see S.C. Shadden, F. Lekien, J.E. Marsden, Definition and Properties of Lagrangian Coherent Structures from Finite-Time Lyapunov Exponents in Two-Dimensional Aperiodic Flows, Physica D, 212(3-4), pp 271--304, 2005). Therefore, there is transport between the coastal region and the ocean. Cinepak (Radius) 55 Mb Direct Lyapunov exponent field computed in backward time. This animation reveals stable structures (i.e., the equivalent of unstable manifolds) and the presence of separation points on the coastline. Cinepak (Radius) 41 Mb 72 Mb The black and white parcels superimposed on the DLE field. The red barrier in the DLE field explains the behaviour of the parcels. The black parcels remains between the structure and the coast. The white parcel was released on the right of the structure and is able to exit the domain. Cinepak (Radius) 23 Mb 50 Mb 37 Mb Elementary pollution control. In this animation, we take advantage of the our ability to predict a qualitative behavior of fluid parcels based on their position with respect to a Lagrangian structure. The black dots represent the motion of pollutants released at a constant rate from an imaginary source on the coastline. The white dots show the evolution of pollutants released by a DLE-aware source. The same amount of pollutant is released in both case but the white source only relase during DLE-friendly intervals. A quantitative analysis shows a reduction of the concentration by a factor 3. Cinepak (Radius) 40 Mb Improved pollution control algorithm. In this animation, a DLE-aware factory determines environmentally-friendly and environmentally-dangerous release periods. Based on this information and the knowledge of its holding tank it determines the best release schedule to minimize both the peaks of maximum concentration in the castal region and the average concentration. Cinepak (Radius) 21 Mb Analysis of the vertical motion of the LCS Screenshot Description Codec This animation shows the entropy spectrum of the motion of the LCS along the coastline during 250 hours. At each time, the last 250 hours of available DLE is used to compute the spectrum. The dominant frequencies (peaks) are used to extrapolate the position of the barrier in the future. Cinepak (Radius) 15 Mb Real-time implementation of the polution control algorithm. The blue vertical line represents the ``present'' time in this animation. The gree vertical line is 8 hours behind and indicates the maximum time for which the LCS can be computed. The black line is the actual latitude of the barrier point and is unknown after the green vertical line. Using the dominant frequencies, the motion of the barrier point is fitted to the last 250 hours of data and extrapolated in time (red curve). Given the estimated position of the barrier point at the present time and the impact of released contaminants. Cinepak (Radius) 15 Mb Comparison with unfiltered data Screenshot Description Codec In the animations above, the velocity field collected by the high-frequency radars is extrapolated to provide a smooth field up to the coastline. In practice, there is a small gap where the velocity vector are unknown. This animation compares the Direct Lyapunov exponent field for the raw radar data (left) and the extrapolated field (right). The structures are identical in both cases as shown in G. Haller,Lagrangian Coherent Structures from Approximate Velocity Data (download PDF ), Phys. Fluids A14, pp 1851--1861, 2002. Cinepak (Radius) 63 Mb Original Direct Lyapunov exponent field computed with the raw radar data. Cinepak (Radius) 8 Mb 36 Mb

 

Selected Figures

Surface currents measured by high-frequency radars reveal eddies moving North along the coast of Florida. The velocity vectors can be used to compute finite-time Lyapunov exponents and simulate particle trajectories. The Finite-Time (Direct) Lyapunov exponent field based on the HF radar data reveal the presence of a sharp (red) Lagrangian Coherent Structure (LCS). Motion of particles are constrained by the motion of the LCS. To exploit our knowledge of the dynamical features in the domain, the entropy spectrum of the motion of the LCS is computed at each time, using 50 hours of data. The same spectrum computed using 75 hours data reveals very little difference and guarantees independence with respect to the integration time (see ShLeMa05) DLE and LCS can only be computed up to 8 hours in the past in a real-time simulation. The dominant frequencies in the spectrum are used to extrapolate the position of the LCS up to the present time. The estimated position of the LCS can be used to determine the impact of polutants released from the coast. LCS-controlled release (dashed curve) reduces the average concentration and the maximum peak of pollutants compared to constant release (solid curve).

 

Citations
This paper is cited by: S.C. Shadden, J.O. Dabiri, J.E. Marsden, Lagrangian Analysis of Fluid Transport in Empirical Vortex Ring Flows, , submitted, 2006.
S.C. Shadden, F. Lekien, J.E. Marsden, Definition and Properties of Lagrangian Coherent Structures from Finite-Time Lyapunov Exponents in Two-Dimensional Aperiodic Flows, Physica D, 212(3-4), pp 271--304, 2005
P. Bhatta, E. Fiorelli, F. Lekien, N.E. Leonard, D.A. Paley, F. Zhang, R. Bachmayer, R.E. Davis, D. Fratantoni, R. Sepulchre, Coordination of an Underwater Glider Fleet for Adaptive Sampling, International Workshop on Underwater Robotics, (in press), pp 61--69, 2005
F. Lekien, G. Haller, Unsteady Flow Separation on Slip Boundaries, J. Fluid Mech., (submitted), 2006
P.F.J. Lermusiaux, F. Lekien, Dynamics and Lagrangian Coherent Structures in the Ocean and their Uncertainty, In Dynamical Systems Methods in Fluid Dynamics, Oberwolfach Workshop. J.E. Marsden and J. Scheurle (Eds), Mathematisches Forschungsinstitut Oberwolfach, 531, pp 19--20, 2005
P.F.J. Lermusiaux, C.-S. Chiu, G.G. Gawarkiewicz, P. Abbot, A.R. Robinson, R.N. Miller, P.J. Haley, W.G. Leslie, S.J. Majumdar, A. Pang, F. Lekien, Quantifying Uncertainties in Ocean Predictions, Oceanography, 49(1), pp 80--88, 2006