Stochastic rectification of fast oscillations on slow manifold closures.
Stochastic rectification of fast oscillations on slow manifold closures.
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DOI：
10.1073/pnas.2113650118
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发表时间：
2021-11-30
影响因子：
11.1
通讯作者：
McWilliams JC
中科院分区：
文献类型：
--
作者：
Chekroun MD;Liu H;McWilliams JC
慢-快系统出现在许多科学应用中，特别是在具有快惯性重力波和慢地转运动的大气和海洋流动中。当慢速变量和快速变量强耦合时--这是从慢速到快速尺度的确定性参数分解的征兆--要得到能够捕捉动态的简化系统仍然是一个挑战。在这里，成功减少这类系统的通用成分被确定，并以典型的大气洛伦兹80模型为例进行了说明。该方法依赖于通过非线性参数化操作的滤波，该参数将完整的动力学分离为其慢动作和快速剩余动力学。后者主要与前者正交，并通过与慢动态无关的随机非线性振子网络来建模。识别慢分量(例如，用于天气预报初始化)和描述慢-快相互作用的问题是地球物理流体动力学的中心问题。在这项研究中，当由于慢地转运动上的快速振荡的爆炸性出现而导致从慢到快的尺度确定性参数化的崩溃时，相关的慢流形闭合的校正问题被讨论。在Lorenz-80模型上，结果表明，如果1)基本流形提供了一个很好的近似最优非线性参数的方法，并且2)流形上的剩余动力学主要与流形垂直，则Mori-zwanzig完全闭包中不需要记忆项。相反，噪声项是解决的关键，在这种情况下，通过随机非线性振子网络获得的与状态无关的噪声被很好地建模。这种随机参数化反过来又允许纠正动量平衡的慢流形，并精确地恢复多尺度动力学。该方法有望进一步应用于强耦合区域中其他更复杂的慢-快系统的闭合。
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.
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DOI：
10.1098/rspa.2014.0963
发表时间：
2015-04-08
期刊：
Proceedings. Mathematical, physical, and engineering sciences
影响因子：
--
作者：
Holm DD
通讯作者：
Holm DD
影响因子：
4
作者：
CAMASSA, R
通讯作者：
CAMASSA, R
影响因子：
2.9
作者：
Froyland, Gary;Junge, Oliver;Koltai, Peter
通讯作者：
Koltai, Peter
影响因子：
1.6
作者：
Cotter, Colin J.;Crisan, Dan;Shevchenko, Igor
通讯作者：
Shevchenko, Igor
影响因子：
1.6
作者：
Chekroun, Mickael D.;Tantet, Alexis;Neelin, J. David
通讯作者：
Neelin, J. David