Large‐scale flows under location uncertainty: a consistent stochastic framework

Abstract

Using a classical example, the Lorenz‐63 model, an original stochastic framework is applied to represent large‐scale geophysical flow dynamics. Rigorously derived from a reformulated material derivative, the proposed framework encompasses several meaningful mechanisms to model geophysical flows. The slightly compressible set‐up, as treated in the Boussinesq approximation, yields a stochastic transport equation for the density and other related thermodynamical variables. Coupled to the momentum equation through a forcing term, the resulting stochastic Lorenz‐63 model is derived consistently. Based on such a reformulated model, the pertinence of this large‐scale stochastic approach is demonstrated over classical eddy‐viscosity based large‐scale representations.

Spatiotemporal Patterns of Chaos in the Atlantic Overturning Circulation

“…These results provide a first estimate of the quantitative accuracy of the AMOC within eddy-resolving ocean-only models. Probabilistic estimates as in Chapron et al (2018) might well represent a useful avenue for further pursuit. This work has been founded by the NSF award OCE1537304 and benefited from interactions with the international CHAOCEAN program lead by Thierry Penduff.…”

Stochastic flow approach to model the mean velocity profile of wall-bounded flows

“…and a null value for the vertical variance tensor (a zz = 0). Integrating (13a) with boundary condition (21) gives an expression for ∂ z u. A second integration of the same equation yields the following velocity profile within the buffer zone…”

“…For isochoric flows with variable density as in geophysical fluid dynamics, interested readers may have a look at [18][19][20]. An application of this framework to derive a stochastic representation of the Lorenz system is also described and studied in [21].…”

Estimation of physical parameters under location uncertainty using an ensemble2–expectation–maximization algorithm

“…The modelling under location uncertainty has been used to derive stochastic expressions of geophysical flows (Resseguier et al ; ; ), efficient reduced‐order flow models (Resseguier et al ; Chapron et al ), and large eddy simulation models for various types of flows (Kadri Harouna and Mémin, ; Chandramouli et al ).…”

“…This imbalance may lead to numerical instability and to the breaking of physical conservation laws, as the variance may increase in an uncontrolled way. In addition, a non‐physical random forcing (i.e., with a form that does not ensue from a physical conservation law) may lead to random dynamics whose low‐noise limit differs significantly from the deterministic original system (Chapron et al ). In other words, the random dynamics converges poorly to the deterministic system for low noise.…”