Computation of rare transitions in the barotropic quasi-geostrophic equations
We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier–Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2015-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/17/1/015009 |
| _version_ | 1797751241755852800 |
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| author | Jason Laurie Freddy Bouchet |
| author_facet | Jason Laurie Freddy Bouchet |
| author_sort | Jason Laurie |
| collection | DOAJ |
| description | We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier–Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager–Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherwise. We adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show that by numerically minimizing an appropriate action functional in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems. |
| first_indexed | 2024-03-12T16:44:38Z |
| format | Article |
| id | doaj.art-8eee4ff302c44f60b64894b8891815d5 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:44:38Z |
| publishDate | 2015-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-8eee4ff302c44f60b64894b8891815d52023-08-08T14:17:20ZengIOP PublishingNew Journal of Physics1367-26302015-01-0117101500910.1088/1367-2630/17/1/015009Computation of rare transitions in the barotropic quasi-geostrophic equationsJason Laurie0Freddy Bouchet1Department of Physics of Complex Systems, Weizmann Institute of Science , 234 Herzl Street, Rehovot, 76100, IsraelLaboratoire de Physique , ENS de Lyon, 46, Allée dʼItalie, F69007, Lyon, FranceWe investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier–Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager–Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherwise. We adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show that by numerically minimizing an appropriate action functional in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems.https://doi.org/10.1088/1367-2630/17/1/015009rare transitionsbistabilityminimum action methodquasi-geostrophic dynamics47.20.Ky47.10.ad |
| spellingShingle | Jason Laurie Freddy Bouchet Computation of rare transitions in the barotropic quasi-geostrophic equations New Journal of Physics rare transitions bistability minimum action method quasi-geostrophic dynamics 47.20.Ky 47.10.ad |
| title | Computation of rare transitions in the barotropic quasi-geostrophic equations |
| title_full | Computation of rare transitions in the barotropic quasi-geostrophic equations |
| title_fullStr | Computation of rare transitions in the barotropic quasi-geostrophic equations |
| title_full_unstemmed | Computation of rare transitions in the barotropic quasi-geostrophic equations |
| title_short | Computation of rare transitions in the barotropic quasi-geostrophic equations |
| title_sort | computation of rare transitions in the barotropic quasi geostrophic equations |
| topic | rare transitions bistability minimum action method quasi-geostrophic dynamics 47.20.Ky 47.10.ad |
| url | https://doi.org/10.1088/1367-2630/17/1/015009 |
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