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: | , |
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Format: | Article |
Language: | English |
Published: |
2012
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Subjects: | |
Online Access: | https://hdl.handle.net/10356/80112 http://hdl.handle.net/10220/8224 |
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Institution: | Nanyang Technological University |
Language: | English |
Summary: | 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. |
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