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Regul. Chaotic Dyn.:

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Regul. Chaotic Dyn., 2018, том 23, выпуск 5, страницы 551–568 (Mi rcd344)  

Эта публикация цитируется в 4 научных статьях (всего в 4 статьях)

The Application of Lagrangian Descriptors to 3D Vector Fields

Víctor J. García-Garridoab, Jezabel Curbeloca, Ana M. Manchoa, Stephen Wigginsd, Carlos R. Mechosoe

a Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, C/Nicolás Cabrera 15, Campus Cantoblanco UAM, 28049, Madrid, Spain
b Departamento de Física y Matemáticas, Universidad de Alcalá, 28871, Alcalá de Henares, Spain
c Departamento de Matemáticas, Facultad de Ciencias Universidad Autónoma de Madrid, 28049, Madrid, Spain
d School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom
e Department of Atmospheric and Oceanic Sciences, University of California at Los Angeles, Los Angeles, CA, USA

Аннотация: Since the 1980s, the application of concepts and ideas from dynamical systems theory to analyze phase space structures has provided a fundamental framework to understand long-term evolution of trajectories in many physical systems. In this context, for the study of fluid transport and mixing the development of Lagrangian techniques that can capture the complex and rich dynamics of time-dependent flows has been crucial. Many of these applications have been to atmospheric and oceanic flows in two-dimensional (2D) relevant scenarios. However, the geometrical structures that constitute the phase space structures in time-dependent three-dimensional (3D) flows require further exploration. In this paper we explore the capability of Lagrangian descriptors (LDs), a tool that has been successfully applied to time-dependent 2D vector fields, to reveal phase space geometrical structures in 3D vector fields. In particular, we show how LDs can be used to reveal phase space structures that govern and mediate phase space transport. We especially highlight the identification of normally hyperbolic invariant manifolds (NHIMs) and tori. We do this by applying this methodology to three specific dynamical systems: a 3D extension of the classical linear saddle system, a 3D extension of the classical Duffing system, and a geophysical fluid dynamics f-plane approximation model which is described by analytical wave solutions of the 3D Euler equations. We show that LDs successfully identify and recover the template of invariant manifolds that define the dynamics in phase space for these examples.

Ключевые слова: Lagrangian descriptors, phase space structure, invariant manifolds, invariant tori, ergodic decomposition

Финансовая поддержка Номер гранта
Office of Naval Research N00014-01-1-0769
Engineering and Physical Sciences Research Council EP/P021123/1
National Science Foundation AGS-1245069
S. Wiggins acknowledges the support of ONR Grant No. N00014-01-1-0769 and EPSRC Grant no. EP/P021123/1. A. M. Mancho acknowledges the support of ONR grant N00014-17-1-3003. V. J. García-Garrido, J.Curbelo and A.M.Mancho thankfully acknowledge the computer resources provided by ICMAT. C.R. Mechoso was supported by the U.S. NSF grant AGS-1245069.


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Тип публикации: Статья
MSC: 37XX, 37D10, 37N10, 37Mxx, 70K43
Поступила в редакцию: 26.06.2018
Принята в печать:30.07.2018
Язык публикации: английский

Образец цитирования: Víctor J. García-Garrido, Jezabel Curbelo, Ana M. Mancho, Stephen Wiggins, Carlos R. Mechoso, “The Application of Lagrangian Descriptors to 3D Vector Fields”, Regul. Chaotic Dyn., 23:5 (2018), 551–568

Цитирование в формате AMSBIB
\by V{\'\i}ctor J. Garc{\'\i}a-Garrido, Jezabel Curbelo, Ana M. Mancho, Stephen Wiggins, Carlos R. Mechoso
\paper The Application of Lagrangian Descriptors to 3D Vector Fields
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 5
\pages 551--568

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    Эта публикация цитируется в следующих статьяx:
    1. Sh. Naik, V. J. Garcia-Garrido, S. Wiggins, “Finding NHIM: identifying high dimensional phase space structures in reaction dynamics using Lagrangian descriptors”, Commun. Nonlinear Sci. Numer. Simul., 79 (2019), UNSP 104907  crossref  mathscinet  isi  scopus
    2. Sh. Naik, S. Wiggins, “Finding normally hyperbolic invariant manifolds in two and three degrees of freedom with Hénon–Heiles-type potential”, Phys. Rev. E, 100:2 (2019), 022204  crossref  mathscinet  isi  scopus
    3. J. Curbelo, C. R. Mechoso, A. M. Mancho, S. Wiggins, “Lagrangian study of the final warming in the southern stratosphere during 2002: Part II. 3D structure”, Clim. Dyn., 53:3-4 (2019), 1277–1286  crossref  isi  scopus
    4. F. Balibrea-Iniesta, J. Xie, V. J. Garcia-Garrido, L. Bertino, A. M. Mancho, S. Wiggins, “Lagrangian transport across the upper arctic waters in the Canada basin”, Q. J. R. Meteorol. Soc., 145:718, A (2019), 76–91  crossref  isi  scopus
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