Lyapunov analysis of multiscale dynamics: the slow bundle of the two-scale Lorenz 96 model
<p>We investigate the geometrical structure of instabilities in the two-scale Lorenz 96 model through the prism of Lyapunov analysis. Our detailed study of the full spectrum of covariant Lyapunov vectors reveals the presence of a <i>slow bundle</i> in tangent space, composed by a s...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2019-05-01
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| Series: | Nonlinear Processes in Geophysics |
| Online Access: | https://www.nonlin-processes-geophys.net/26/73/2019/npg-26-73-2019.pdf |
| Summary: | <p>We investigate the geometrical structure of instabilities in the two-scale
Lorenz 96 model through the prism of Lyapunov analysis. Our detailed study of
the full spectrum of covariant Lyapunov vectors reveals the presence of a
<i>slow bundle</i> in tangent space, composed by a set of vectors with a
significant projection onto the slow degrees of freedom; they correspond
to the smallest (in absolute value) Lyapunov exponents and thereby to the
longer timescales. We show that the dimension of the slow bundle is extensive
in the number of both slow and fast degrees of freedom and discuss its
relationship with the results of a finite-size analysis of instabilities,
supporting the conjecture that the slow-variable behavior is effectively
determined by a nontrivial subset of degrees of freedom. More precisely, we
show that the slow bundle corresponds to the Lyapunov spectrum region where
fast and slow instability rates overlap, “mixing” their evolution into a
set of vectors which simultaneously carry information on both scales. We
suggest that these results may pave the way for future applications to
ensemble forecasting and data assimilations in weather and climate models.</p> |
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| ISSN: | 1023-5809 1607-7946 |