Department of Atmospheric & Oceanic Sciences, University of California, Los Angeles, CA 90095-1565.
Department of Earth and Planetary Sciences, Weizmann Institute, Rehovot 76100, Israel.
Proc Natl Acad Sci U S A. 2021 Nov 30;118(48). doi: 10.1073/pnas.2113650118.
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.
识别慢变分量（例如，用于天气预报初始化）和刻画慢变-快变相互作用的问题是地球物理流体动力学的核心问题。在这项研究中，当由于快变振荡在慢变、地转运动上的爆发性出现而导致慢变-快变尺度确定性参数化失效时，解决了与之相关的慢流形闭合的校正问题。对于这种情况，在 Lorenz 80 模型上的研究表明，如果 1）底层流形提供了对平均快变量的最优非线性参数化的良好逼近，并且 2）在这个流形之外的残差动力学主要与其正交，那么在 Mori-Zwanzig 全闭中就不需要记忆项。相反，噪声项是需要解决的关键，并且在这种情况下，通过随机非线性振荡器的网络，可以很好地用状态独立的噪声来建模。这种随机参数化反过来允许校正动量平衡的慢流形，并准确地恢复多尺度动力学。该方法有望进一步应用于强耦合状态下其他更复杂的慢变-快变系统的闭合。
