A dynamical systems perspective for a real-time response to a marine oil spill

García-Garrido, Víctor J.; Ramos, Antonio G.; Mancho, Ana M.; Coca, Josep; Wiggins, Stephen

doi:10.1016/j.marpolbul.2016.08.018

Cited by 39 publications

(37 citation statements)

References 46 publications

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“…It also applies to both Hamiltonian and non-Hamiltonian systems 52 as well as to stochastic dynamical systems 53 . Moreover, Lagrangian descriptors can be applied directly to data sets obtained from the numerical solution of geophysical models and satelite observations [54][55][56] . We provide more details on our use of Lagrangian descriptors in Appendix A.…”

Section: Introductionmentioning

confidence: 99%

Tilting and Squeezing: Phase Space Geometry of Hamiltonian Saddle-Node Bifurcation and its Influence on Chemical Reaction Dynamics

García-Garrido

Naik

Wiggins

2020

Int. J. Bifurcation Chaos

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In this article we present the influence of a Hamiltonian saddle-node bifurcation on the highdimensional phase space structures that mediate reaction dynamics. To achieve this goal, we identify the phase space invariant manifolds using Lagrangian descriptors, which is a trajectorybased diagnostic suitable for the construction of a complete "phase space tomography" by means of analyzing dynamics on low-dimensional slices. First, we build a Hamiltonian system with one degree-of-freedom (DoF) that models reaction, and study the effect of adding a parameter to the potential energy function that controls the depth of the well. Then, we extend this framework to a saddle-node bifurcation for a two DoF Hamiltonian, constructed by coupling a harmonic oscillator, i.e. a bath mode, to the other reactive DoF in the system. For this problem, we describe the phase space structures associated with the rank-1 saddle equilibrium point in the bottleneck region, which is a Normally Hyperbolic Invariant Manifold (NHIM) and its stable and unstable manifolds.Finally, we address the qualitative changes in the reaction dynamics of the Hamiltonian system due to changes in the well depth of the potential energy surface that gives rise to the saddle-node bifurcation.

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Section: Introductionmentioning

confidence: 99%

Tilting and Squeezing: Phase Space Geometry of Hamiltonian Saddle-Node Bifurcation and its Influence on Chemical Reaction Dynamics

García-Garrido

Naik

Wiggins

2020

Int. J. Bifurcation Chaos

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“…Perturbation of the cat eyes results in irreversible deformation of material contours, signifying Rossby wave breaking. de la Cámara et al (2013) and Guha et al (2016) identified HTs both within and outside the SPV, thus suggesting that Rossby wave breaking can occur in either of those regions. The former authors worked with reanalysis data, while Guha et al (2016) used a dynamical model based on the shallow-water equations in which the perturbing waves are produced in a controlled manner.…”

Section: Will Ozone Depletion Extend Worldwide?mentioning

confidence: 98%

REsponse to anonymous referee #1

Mancho¹

2017

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/userguides/explore-bristol-research/ebr-terms/ Abstract. In this work, we study the Lagrangian footprint of the planetary waves present in the Southern Hemisphere stratosphere during the exceptional sudden Stratospheric warming event that took place during September 2002. Our focus is on constructing a simple kinematic model that retains the fundamental mechanisms responsible for complex fluid parcel evolution, during the polar vortex breakdown and its previous stages. The construction of the kinematic model is guided by the Fourier decomposition of the geopotential field. The study of Lagrangian transport phenomena in the ERA-Interim reanalysis data highlights hyperbolic trajectories, and these trajectories are Lagrangian objects that are the kinematic mechanism for the observed filamentation phenomena. Our analysis shows that the breaking and splitting of the polar vortex is justified in our model by the sudden growth of a planetary wave and the decay of the axisymmetric flow.

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“…The function M has been applied in a variety of geophysical contexts. For example, in the ocean, it has been used to analyse the structure of the Kuroshio current (Mendoza and Mancho, 2012), to discuss the performance of different oceanic data sets (Mendoza et al, 2014), to analyse and develop search and rescue strategies at sea (García-Garrido et al, 2015) and to efficiently manage in real time the environmental impact of marine oil spills (García-Garrido et al, 2016). In the field of atmospheric sciences, M has been used to study transport processes across the southern SPV and RWB de la Cá-mara et al, 2012Cá-mara et al, , 2013Smith and McDonald, 2014;Guha et al, 2016 and to investigate the Northern Hemisphere major stratospheric final warming in 2016 (Manney and Lawrence, 2016).…”

Section: Lagrangian Descriptorsmentioning

confidence: 99%

A simple kinematic model for the Lagrangian description of relevant nonlinear processes in the stratospheric polar vortex

García-Garrido¹,

Curbelo

Mechoso

et al. 2017

Nonlin. Processes Geophys.

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Abstract. In this work, we study the Lagrangian footprint of the planetary waves present in the Southern Hemisphere stratosphere during the exceptional sudden Stratospheric warming event that took place during September 2002. Our focus is on constructing a simple kinematic model that retains the fundamental mechanisms responsible for complex fluid parcel evolution, during the polar vortex breakdown and its previous stages. The construction of the kinematic model is guided by the Fourier decomposition of the geopotential field. The study of Lagrangian transport phenomena in the ERA-Interim reanalysis data highlights hyperbolic trajectories, and these trajectories are Lagrangian objects that are the kinematic mechanism for the observed filamentation phenomena. Our analysis shows that the breaking and splitting of the polar vortex is justified in our model by the sudden growth of a planetary wave and the decay of the axisymmetric flow.

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A dynamical systems perspective for a real-time response to a marine oil spill

Cited by 39 publications

References 46 publications

Tilting and Squeezing: Phase Space Geometry of Hamiltonian Saddle-Node Bifurcation and its Influence on Chemical Reaction Dynamics

Tilting and Squeezing: Phase Space Geometry of Hamiltonian Saddle-Node Bifurcation and its Influence on Chemical Reaction Dynamics

REsponse to anonymous referee #1

A simple kinematic model for the Lagrangian description of relevant nonlinear processes in the stratospheric polar vortex

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