期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2021
卷号：118
期号：48
DOI：10.1073/pnas.2113650118
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Significance
Slow–fast systems arise in many scientific applications, in particular in atmospheric and oceanic flows with fast inertia–gravity waves and slow geostrophic motions. When the slow and fast variables are strongly coupled—symptomatic of breakdown of slow-to-fast scales deterministic parameterizations—it remains a challenge to derive reduced systems able to capture the dynamics. Here, generic ingredients for successful reduction of such systems are identified and illustrated for the paradigmatic atmospheric Lorenz 80 model. The approach relies on a filtering operated through a nonlinear parameterization that separates the full dynamics into its slow motion and fast residual dynamics. The latter is mainly orthogonal to the former and is modeled via networks of stochastic nonlinear oscillators, independent of the slow dynamics.
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.
关键词：multiscale chaos; stochastic parameterization; multiscale closure; slow manifold; fast oscillations
