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| Titel |
A statistical mechanics approach to computing rare transitions in multi-stable turbulent geophysical flows |
| VerfasserIn |
J. Laurie, F. Bouchet |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250069305
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| Zusammenfassung |
| Many turbulent flows undergo sporadic random transitions, after long periods of apparent
statistical stationarity. For instance, paths of the Kuroshio [1], the Earth’s magnetic field
reversal, atmospheric flows [2], MHD experiments [3], 2D turbulence experiments [4,5], 3D
flows [6] show this kind of behavior. The understanding of this phenomena is extremely
difficult due to the complexity, the large number of degrees of freedom, and the
non-equilibrium nature of these turbulent flows. It is however a key issue for many
geophysical problems.
A straightforward study of these transitions, through a direct numerical simulation of the
governing equations, is nearly always impracticable. This is mainly a complexity problem,
due to the large number of degrees of freedom involved for genuine turbulent flows, and the
extremely long time between two transitions.
In this talk, we consider two-dimensional and geostrophic turbulent models, with
stochastic forces. We consider regimes where two or more attractors coexist. As an alternative
to direct numerical simulation, we propose a non-equilibrium statistical mechanics approach
to the computation of this phenomenon. Our strategy is based on large deviation theory [7],
derived from a path integral representation of the stochastic process. Among the trajectories
connecting two non-equilibrium attractors, we determine the most probable one. Moreover,
we also determine the transition rates, and in which cases this most probable trajectory is a
typical one.
Interestingly, we prove that in the class of models we consider, a mechanism exists for
diffusion over sets of connected attractors. For the type of stochastic forces that allows this
diffusion, the transition between attractors is not a rare event. It is then very difficult to
characterize the flow as bistable. However for another class of stochastic forces,
this diffusion mechanism is prevented, and genuine bistability or multi-stability is
observed.
We discuss how these results are probably connected to the long debated existence of
multi-stability in the atmosphere and oceans.
References
[1]Â Â Â M. J. Schmeits and H. A. Dijkstra: Bimodal behavior of the Kuroshio and the
Gulf stream. J. Phys. Oceanogr. 31:3435–3456, 2001.
[2]Â Â Â E. R. Weeks, Y. Tian, J. S. Urbach, K. Ide, H. L. Swinney and M. Ghil:
Transitions between blocked and zonal flows in a rotating annulus with topography.
Science 278:1598–1601, 1997.
[3]Â Â Â M. Berhanu et al.: Magnetic field reversals in an experimental turbulent
dynamo. Europhys. Lett. 77:59001, 2007.
[4]Â Â Â J. Sommeria: Experimental study of the two-dimensional inverse energy
cascade in a square box. J. Fluid Mech. 170:139–168, 1986.
[5]Â Â Â S. R. Maassen, H. J. H. Clercx and G. J. F. van Heijst: Self-organization
of decaying quasi-two-dimensional turbulence in stratified fluid in rectangular
containers. J. Fluid Mech. 495:19–33, 2003.
[6]Â Â Â F. Ravelet, L. Marié, A. Chiffaudel and F. Daviaud: Multistability and memory
effect in a highly turbulent flow: experimental evidence for a global bifurcation.
Phys. Rev. Lett. 93:164501, 2004.
[7]Â Â Â M. I. Freidlin and A. D. Wentzell: Random perturbations of dynamical systems.
2nd ed. Springer, New York, 1998. |
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