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Stochastic rectification of fast oscillations on slow manifold closures

The problems of identifying the slow component (e.g., for weather forecast initialization) and of characterizing slow–fast interactions are central to geophysical fluid dynamics. In this study, the related rectification problem of slow manifold closures is addressed when breakdown of slow-to-fast sc...

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Autores principales: Chekroun, Mickaël D., Liu, Honghu, McWilliams, James C.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: National Academy of Sciences 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8640743/
https://www.ncbi.nlm.nih.gov/pubmed/34819377
http://dx.doi.org/10.1073/pnas.2113650118
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author Chekroun, Mickaël D.
Liu, Honghu
McWilliams, James C.
author_facet Chekroun, Mickaël D.
Liu, Honghu
McWilliams, James C.
author_sort Chekroun, Mickaël D.
collection PubMed
description The problems of identifying the slow component (e.g., for weather forecast initialization) and of characterizing slow–fast interactions are central to geophysical fluid dynamics. In this study, the related rectification problem of slow manifold closures is addressed when breakdown of slow-to-fast scales deterministic parameterizations occurs due to explosive emergence of fast oscillations on the slow, geostrophic motion. For such regimes, it is shown on the Lorenz 80 model that if 1) the underlying manifold provides a good approximation of the optimal nonlinear parameterization that averages out the fast variables and 2) the residual dynamics off this manifold is mainly orthogonal to it, then no memory terms are required in the Mori–Zwanzig full closure. Instead, the noise term is key to resolve, and is shown to be, in this case, well modeled by a state-independent noise, obtained by means of networks of stochastic nonlinear oscillators. This stochastic parameterization allows, in turn, for rectifying the momentum-balanced slow manifold, and for accurate recovery of the multiscale dynamics. The approach is promising to be further applied to the closure of other more complex slow–fast systems, in strongly coupled regimes.
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spelling pubmed-86407432021-12-13 Stochastic rectification of fast oscillations on slow manifold closures Chekroun, Mickaël D. Liu, Honghu McWilliams, James C. Proc Natl Acad Sci U S A Physical Sciences The problems of identifying the slow component (e.g., for weather forecast initialization) and of characterizing slow–fast interactions are central to geophysical fluid dynamics. In this study, the related rectification problem of slow manifold closures is addressed when breakdown of slow-to-fast scales deterministic parameterizations occurs due to explosive emergence of fast oscillations on the slow, geostrophic motion. For such regimes, it is shown on the Lorenz 80 model that if 1) the underlying manifold provides a good approximation of the optimal nonlinear parameterization that averages out the fast variables and 2) the residual dynamics off this manifold is mainly orthogonal to it, then no memory terms are required in the Mori–Zwanzig full closure. Instead, the noise term is key to resolve, and is shown to be, in this case, well modeled by a state-independent noise, obtained by means of networks of stochastic nonlinear oscillators. This stochastic parameterization allows, in turn, for rectifying the momentum-balanced slow manifold, and for accurate recovery of the multiscale dynamics. The approach is promising to be further applied to the closure of other more complex slow–fast systems, in strongly coupled regimes. National Academy of Sciences 2021-11-23 2021-11-30 /pmc/articles/PMC8640743/ /pubmed/34819377 http://dx.doi.org/10.1073/pnas.2113650118 Text en https://creativecommons.org/licenses/by-nc-nd/4.0/This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND) (https://creativecommons.org/licenses/by-nc-nd/4.0/) .
spellingShingle Physical Sciences
Chekroun, Mickaël D.
Liu, Honghu
McWilliams, James C.
Stochastic rectification of fast oscillations on slow manifold closures
title Stochastic rectification of fast oscillations on slow manifold closures
title_full Stochastic rectification of fast oscillations on slow manifold closures
title_fullStr Stochastic rectification of fast oscillations on slow manifold closures
title_full_unstemmed Stochastic rectification of fast oscillations on slow manifold closures
title_short Stochastic rectification of fast oscillations on slow manifold closures
title_sort stochastic rectification of fast oscillations on slow manifold closures
topic Physical Sciences
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8640743/
https://www.ncbi.nlm.nih.gov/pubmed/34819377
http://dx.doi.org/10.1073/pnas.2113650118
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