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Review Article: the Lagrangian Description of Aperiodic Flows: a Case Study of the Kuroshio Current : Volume 19, Issue 4 (21/08/2012)

By Mendoza, C.

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Book Id: WPLBN0003973394
Format Type: PDF Article :
File Size: Pages 24
Reproduction Date: 2015

Title: Review Article: the Lagrangian Description of Aperiodic Flows: a Case Study of the Kuroshio Current : Volume 19, Issue 4 (21/08/2012)  
Author: Mendoza, C.
Volume: Vol. 19, Issue 4
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Historic
Publication Date:
2012
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Mendoza, C., & Mancho, A. M. (2012). Review Article: the Lagrangian Description of Aperiodic Flows: a Case Study of the Kuroshio Current : Volume 19, Issue 4 (21/08/2012). Retrieved from http://hawaiilibrary.net/


Description
Description: Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, C/ Nicolás Cabrera 15, Campus Cantoblanco UAM, 28049, Madrid, Spain. This article reviews several recently developed Lagrangian tools and shows how their combined use succeeds in obtaining a detailed description of purely advective transport events in general aperiodic flows. In particular, because of the climate impact of ocean transport processes, we illustrate a 2-D application on altimeter data sets over the area of the Kuroshio Current, although the proposed techniques are general and applicable to arbitrary time dependent aperiodic flows. The first challenge for describing transport in aperiodical time dependent flows is obtaining a representation of the phase portrait where the most relevant dynamical features may be identified. areas that are related to confinement regions. This representation is accomplished by using global Lagrangian descriptors that when applied for instance to the altimeter data sets retrieve over the ocean surface a phase portrait where the geometry of interconnected dynamical systems is visible. The phase portrait picture is essential because it evinces which transport routes are acting on the whole flow. Once these routes are roughly recognised, it is possible to complete a detailed description by the direct computation of the finite time stable and unstable manifolds of special hyperbolic trajectories that act as organising centres of the flow.

Summary
Review Article: The Lagrangian description of aperiodic flows: a case study of the Kuroshio Current

Excerpt
Hernández-Carrasco, I., Hernández-Garc\'ia, E., López, C., and Turiel., A.: How reliable are finite-size Lyapunov exponents for the assessment of ocean dynamics?, Ocean Model., 36, 208–218, 2011.; Ide, K., Small, D., and Wiggins, S.: Distinguished hyperbolic trajectories in time-dependent fluid flows: analytical and computational approach for velocity fields defined as data sets, Nonlin. Processes Geophys., 9, 237–263, doi:10.5194/npg-9-237-2002, 2002.; Joseph, B. and Legras, B.: Relation between Kinematic Boundaries, Stirring, and Barriers for the Antarctic Polar Vortex, J. Atmos. Sci., 59, 1198–1212, 2002.; Ju, N., Small, D., and Wiggins, S.: Existence and computation of hyperbolic trajectories of aperiodically time dependent vector fields and their approximations, Int. J. Bifurcation Chaos Appl. Sci. Eng., 13, 1449–1457, 2003.; Kuznetsov, L., Toner, M., Kirwan, A. D., and Jones, C.: The Loop Current and adjacent rings delineated by Lagrangian analysis of the near-surface flow, J. Mar. Res., 60, 405–429, 2002.; Larnicol, G., Guinehut, S., Rio, M. H., Drevillon, M., Faugere, Y., and Nicolas, G.: The global observed ocean products of the French Mercator project., Proceedings of the 15 years of progress in Radar altimetry, ESA symposium, Venice, March, 2006.; Lehahn, Y., d'Ovidio, F., Levy, M., and Heifetz, E.: Stirring of the Northeast Atlantic spring bloom: a Lagrangian analysis based on multi-satellite data, J. Geophys. Res., 112, C08005, doi:10.1029/2006JC003927, 2007.; Madrid, J. A. J. and Mancho, A. M.: Distinguished trajectories in time dependent vector fields, Chaos, 19, 013111, doi:10.1063/1.3056050, 2009.; Malhotra, N. and Wiggins, S.: Geometric structures, lobe dynamics, and Lagrangian transport in flows with aperiodic timedependence, with applications to Rossby wave flow, J. Nonlin. Sci., 8, 401–456, 1998.; Malhotra, N., Mezic, I., and Wiggins, S.: Patchiness: A new diagnostic for Lagrangian trajectory analysis in time-dependent fluid flows, Int. J. Bifurcation Chaos, 8, 1053–1093, 1998.; Mancho, A. M., Small, D., Wiggins, S., and Ide, K.: Computation of stable and unstable manifolds of hyperbolic trajectories in two-dimensional, aperiodically time-dependent vector fields, Physica D, 182, 188–222, 2003.; Mancho, A. M., Small, D., and Wiggins, S.: Computation of hyperbolic trajectories and their stable and unstable manifolds for oceanographic flows represented as data sets, Nonlin. Processes Geophys., 11, 17–33, doi:10.5194/npg-11-17-2004, 2004.; Mancho, A. M., Small, D., and Wiggins, S.: A comparison of methods for interpolating chaotic flows from discrete velocity data, Comp. Fluids, 35, 416–428, 2006{a}.; Mancho, A. M., Small, D., and Wiggins, S.: A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: Theoretical and computational issues, Phys. Rep., 437, 55–124, 2006{b}.; Mancho, A. M., Hernández-Garc\'ia, E., Small, D., and Wiggins, S.: Lagrangian Transport through an Ocean Front in the Northwestern Mediterranean Sea, J. Phys. Oceanogr., 38, 1222–1237, 2008.; Mancho, A. M., Wiggins, S., Curbelo, J., and Mendoza, C.: The phase portrait of aperiodic non-autonomous dynamical systems, http://arxiv.org/abs/1106.1306, 2012.; Mendoza, C. and Mancho, A. M.: The hidden geometry of ocean flows, Phys. Rev. Lett., 105, 038501–1–038501–4, 2010.; Mendoza, C., Mancho, A. M., and Rio, M.-H.: The turnstile mechanism across the Kuroshio current: analysis of dynamics in altimeter velocity fields, Nonlin. Processes Geophys., 17, 103–111,

 

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