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Fluids 2018, 3(1), 21; https://doi.org/10.3390/fluids3010021

Multiscale Stuart-Landau Emulators: Application to Wind-Driven Ocean Gyres

1
Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, CA 90095, USA
2
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
*
Author to whom correspondence should be addressed.
Received: 13 February 2018 / Revised: 27 February 2018 / Accepted: 28 February 2018 / Published: 6 March 2018
(This article belongs to the Special Issue Reduced Order Modeling of Fluid Flows)
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Abstract

The multiscale variability of the ocean circulation due to its nonlinear dynamics remains a big challenge for theoretical understanding and practical ocean modeling. This paper demonstrates how the data-adaptive harmonic (DAH) decomposition and inverse stochastic modeling techniques introduced in (Chekroun and Kondrashov, (2017), Chaos, 27), allow for reproducing with high fidelity the main statistical properties of multiscale variability in a coarse-grained eddy-resolving ocean flow. This fully-data-driven approach relies on extraction of frequency-ranked time-dependent coefficients describing the evolution of spatio-temporal DAH modes (DAHMs) in the oceanic flow data. In turn, the time series of these coefficients are efficiently modeled by a family of low-order stochastic differential equations (SDEs) stacked per frequency, involving a fixed set of predictor functions and a small number of model coefficients. These SDEs take the form of stochastic oscillators, identified as multilayer Stuart–Landau models (MSLMs), and their use is justified by relying on the theory of Ruelle–Pollicott resonances. The good modeling skills shown by the resulting DAH-MSLM emulators demonstrates the feasibility of using a network of stochastic oscillators for the modeling of geophysical turbulence. In a certain sense, the original quasiperiodic Landau view of turbulence, with the amendment of the inclusion of stochasticity, may be well suited to describe turbulence. View Full-Text
Keywords: cross-correlations; eddy-resolving; Hankel matrices; inverse modeling; low-frequency variability; Ruelle–Pollicott resonances; stochastic modeling; stochastic oscillators cross-correlations; eddy-resolving; Hankel matrices; inverse modeling; low-frequency variability; Ruelle–Pollicott resonances; stochastic modeling; stochastic oscillators
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Kondrashov, D.; Chekroun, M.D.; Berloff, P. Multiscale Stuart-Landau Emulators: Application to Wind-Driven Ocean Gyres. Fluids 2018, 3, 21.

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