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

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.

Variational Approach to Closure of Nonlinear Dynamical Systems: Autonomous Case

“…Once R is approximated from an optimal PM, the practical determination of the memory and stochastic term could also benefit from the data-driven modeling techniques of [CK17], to model the residual,ẏ c − R(y c ), where y c denotes the low-mode projection of a fully resolved solution y. As illustrated and discussed in [KCB18] for a wind-driven ocean gyres model, the data-driven techniques of [CK17] have been successfully applied to model the coarse-scale dynamics. To operate in practice, the data-driven techniques of [CK17] require observations of y(t) of length comparable also to a decorrelation time of the dynamics [CK17, KCG18,KCYG18], as for the optimization of the dynamically-based PMs of Sec.…”

“…Landau [LL59] and Hopf [Hop48] suggested that turbulence is the result of an infinite sequence of bifurcations, each adding another independent period to a quasi-periodic motion of increasingly greater complexity. More recently, it has been shown numerically that the original quasiperiodic Landau's view of turbulence, with the amendment of the inclusion of stochasticity, may be well suited to describe certain turbulent behavior [KCB18], at least for the motion of large eddies. In the 1970's it has been theoretically argued and confirmed by many experiments that dynamical systems may exhibit strange attractors which result in chaotic but deterministic behavior after a (very) few bifurcations have taken place.…”

Physically constrained data‐driven correction for reduced‐order modeling of fluid flows

“…We note that data‐driven closure modeling for non‐ROM settings is an extremely active research area (see, eg, the works of Duraisamy et al and Ling et al). We also note that there are other DD‐ROM closure models . We emphasize, however, that these DD‐ROM closure models are different from our DDC‐ROM in the following respects.…”

“…We also note that there are other DD-ROM closure models. [30][31][32][33][34][35][36][37] We emphasize, however, that these DD-ROM closure models are different from our DDC-ROM in the following respects.…”

A Hybrid Approach for Model Order Reduction of Barotropic Quasi-Geostrophic Turbulence

“…Since ocean circulation is a significant part of climate systems, it is extremely important to study and understand the underlying physics to get the benefits from the rich potential of oceans. There have been many efforts put on developing models for ocean dynamics in the last few decades [8][9][10][11][12][13]. However, it is computationally challenging to model the ocean dynamics because of its large range of spatiotemporal scales and sporadic random transitions between coexisting eddies and vortices [14,15].…”