Hyperbolic lines and the stratospheric polar vortex

The necessary and sufficient conditions for Lagrangian hyperbolicity recently derived in the literature are reviewed in the light of older concepts of effective local rotation in strain coordinates. In particular, we introduce the simple interpretation of the necessary condition as a c...

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Main Authors: Koh, Tieh Yong., Legras, Bernard.
Format: Article
Language:English
Published: 2012
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Online Access:https://hdl.handle.net/10356/80112
http://hdl.handle.net/10220/8224
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-801122020-09-26T21:31:30Z Hyperbolic lines and the stratospheric polar vortex Koh, Tieh Yong. Legras, Bernard. DRNTU::Science::Geology The necessary and sufficient conditions for Lagrangian hyperbolicity recently derived in the literature are reviewed in the light of older concepts of effective local rotation in strain coordinates. In particular, we introduce the simple interpretation of the necessary condition as a constraint on the local angular displacement in strain coordinates. These mathematically rigorous conditions are applied to the winter stratospheric circulation of the southern hemisphere, using analyzed wind data from the European Center for Medium-Range Weather Forecasts. Our results demonstrate that the sufficient condition is too strong and the necessary condition is too weak, so that both conditions fail to identify hyperbolic lines in the stratosphere. However a phenomenological, nonrigorous, criterion based on the necessary condition reveals the hyperbolic structure of the flow. Another still nonrigorous alternative is the finite-size Lyapunov exponent FSLE which is shown to produce good candidates for hyperbolic lines. In addition, we also tested the sufficient condition for Lagrangian ellipticity and found that it is too weak to detect elliptic coherent structures ECS in the stratosphere, of which the polar vortex is an obvious candidate. Yet, the FSLE method reveals a clear ECS-like barrier to mixing along the polar vortex edge. Further theoretical advancement is needed to explain the apparent success of nonrigorous methods, such as the FSLE approach, so as to achieve a sound kinematic understanding of chaotic mixing in the winter stratosphere and other geophysical flows. Published version 2012-06-20T08:57:43Z 2019-12-06T13:40:56Z 2012-06-20T08:57:43Z 2019-12-06T13:40:56Z 2002 2002 Journal Article Koh, T. Y., & Legras, B. (2002). Hyperbolic lines and the stratospheric polar vortex. Chaos, 12(2), 382-394. 1054-1500 https://hdl.handle.net/10356/80112 http://hdl.handle.net/10220/8224 10.1063/1.1480442 en Chaos © 2002 American Institute of Physics. This paper was published in Chaos and is made available as an electronic reprint (preprint) with permission of American Institute of Physics. The paper can be found at the following official URL: [http://dx.doi.org/10.1063/1.1480442]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. 13 p. application/pdf
institution Nanyang Technological University
building NTU Library
country Singapore
collection DR-NTU
language English
topic DRNTU::Science::Geology
spellingShingle DRNTU::Science::Geology
Koh, Tieh Yong.
Legras, Bernard.
Hyperbolic lines and the stratospheric polar vortex
description The necessary and sufficient conditions for Lagrangian hyperbolicity recently derived in the literature are reviewed in the light of older concepts of effective local rotation in strain coordinates. In particular, we introduce the simple interpretation of the necessary condition as a constraint on the local angular displacement in strain coordinates. These mathematically rigorous conditions are applied to the winter stratospheric circulation of the southern hemisphere, using analyzed wind data from the European Center for Medium-Range Weather Forecasts. Our results demonstrate that the sufficient condition is too strong and the necessary condition is too weak, so that both conditions fail to identify hyperbolic lines in the stratosphere. However a phenomenological, nonrigorous, criterion based on the necessary condition reveals the hyperbolic structure of the flow. Another still nonrigorous alternative is the finite-size Lyapunov exponent FSLE which is shown to produce good candidates for hyperbolic lines. In addition, we also tested the sufficient condition for Lagrangian ellipticity and found that it is too weak to detect elliptic coherent structures ECS in the stratosphere, of which the polar vortex is an obvious candidate. Yet, the FSLE method reveals a clear ECS-like barrier to mixing along the polar vortex edge. Further theoretical advancement is needed to explain the apparent success of nonrigorous methods, such as the FSLE approach, so as to achieve a sound kinematic understanding of chaotic mixing in the winter stratosphere and other geophysical flows.
format Article
author Koh, Tieh Yong.
Legras, Bernard.
author_facet Koh, Tieh Yong.
Legras, Bernard.
author_sort Koh, Tieh Yong.
title Hyperbolic lines and the stratospheric polar vortex
title_short Hyperbolic lines and the stratospheric polar vortex
title_full Hyperbolic lines and the stratospheric polar vortex
title_fullStr Hyperbolic lines and the stratospheric polar vortex
title_full_unstemmed Hyperbolic lines and the stratospheric polar vortex
title_sort hyperbolic lines and the stratospheric polar vortex
publishDate 2012
url https://hdl.handle.net/10356/80112
http://hdl.handle.net/10220/8224
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