Deciphering the Role of Small-Scale Inhomogeneity on Geophysical Flow Structuration: A Stochastic Approach

Bauer, Werner; Chandramouli, Pranav; Chapron, Bertrand; Li, Long; Mémin, Étienne

doi:10.1175/jpo-d-19-0164.1

Cited by 35 publications

(84 citation statements)

References 52 publications

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“…Note that d t θ = θ t+dt − θ t stands for the forward time-increment of the scalar θ at a fixed point x. The turbophoresis term, u s = 1 2 ∇• a, accounting for the effect of statistical inhomogeneity of the small-scale field on the largescale current, is referred to as the Itô-Stokes drift in Bauer et al (2020). This term was shown to play a crucial role in the transition from the viscous layer regime to the logarithmic layer regime in wall bounded turbulent flows (Pinier et al, 2019).…”

Section: Stochastic Barotropic Vorticity Equationmentioning

confidence: 99%

“…The process dM t gathers the additional momentum terms introduced in the stochastic transport equation (3.4b). Due to the geostrophic balance and the Doob-Meyer decomposition theorem (Kunita, 1997), the small-scale flow is defined from a random stream function ϕdB t as σdB t = ∇ ⊥ ϕdB t (Bauer et al, 2020). The curl of such a process can be expanded as…”

Section: Stochastic Barotropic Vorticity Equationmentioning

confidence: 99%

“…As discussed above, this ability is essential for data assimilation applications. Recently, a stochastic barotropic quasi-geostrophic (QG) model has been proposed (Bauer et al, 2020) within this setting to study the structuration effect of the random field on the large-scale flow. Numerical results illustrate that, encoding an inhomogeneous random component into a propagating monochromatic Rossby wave, induces the formation of extra large vortices.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic representation of mesoscale eddy effects in coarse-resolution barotropic models

Bauer

Chandramouli

et al. 2020

Ocean Modelling

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A stochastic representation based on a physical transport principle is proposed to account for mesoscale eddy effects on the evolution of the large-scale flow. This framework arises from a decomposition of the Lagrangian velocity into a smooth in time component and a highly oscillating term. One important characteristic of this random model is that it conserves the energy of any transported scalar. Such an energy-preserving representation is tested for the coarse simulation of a barotropic circulation in a shallow ocean basin, driven by a symmetric double-gyres wind forcing. The empirical spatial correlation of the random small-scale velocity is estimated from data of an eddy-resolving simulation. After reaching a turbulent equilibrium state, a statistical analysis of tracers shows that the proposed random model enables us to reproduce accurately, on a coarse mesh, the local structures of the first four statistical moments (mean, variance, skewness and kurtosis) of the high-resolution eddy-resolved data.

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Section: Stochastic Barotropic Vorticity Equationmentioning

confidence: 99%

Section: Stochastic Barotropic Vorticity Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stochastic representation of mesoscale eddy effects in coarse-resolution barotropic models

Bauer

Chandramouli

et al. 2020

Ocean Modelling

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“…Both deformation rate and rotation-rate contribute to diffusion, unlike in the classical eddy-viscosity model. Turbulent compressibility: the continuity Equation (20) suggests that the flow is turbulent-compressible; i.e., the unresolved turbulence induces a local fluid compression or expansion.…”

Section: Physical Interpretationmentioning

confidence: 99%

“…The LU model was tested in several cases: in a series of papers Resseguier et al [16][17][18][19], as well as Bauer et al [20,21], successfully used this model to study geophysical flows. It was found to be more accurate in the reproduction of extreme events and to provide a new analysis tool.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Modelling of Turbulent Flows for Numerical Simulations

Cintolesi

Mémin

2020

Fluids

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Numerical simulations are a powerful tool to investigate turbulent flows, both for theoretical studies and practical applications. The reliability of a simulation is mainly dependent on the turbulence model adopted, and improving its accuracy is a crucial issue. In this study, we investigated the potential for an alternative formulation of the Navier–Stokes equations, based on the stochastic representation of the velocity field. The new approach, named pseudo-stochastic simulation (PSS), is a generalisation of the widespread classical eddy–viscosity model, where the contribution of the unresolved scales of motion is expressed by a variance tensor, modelled following different paradigms. The PSS models were compared with the classical ones mathematically and numerically in the turbulent channel flow at R e τ = 590 . The PSS and the classical models are equivalent when the variance tensor is shaped through a molecular dissipation analogy, while it is more accurate when the tensor is defined by the way of a local variance model. A near-wall damping function derived from recent advancement in the field is also proposed and was successfully validated. The analyses demonstrate the relevance of the approach proposed and provide a basis for the development of an alternative turbulence model.

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Stochastic parametrization: An alternative to inflation in ensemble Kalman filters

Dufée

Mémin

Crisan

2022

Quart J Royal Meteoro Soc

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We investigate the application of a stochastic dynamical model in ensemble Kalman filter methods. Ensemble Kalman filters are very popular in data assimilation because of their ability to handle the filtering of high-dimensional systems with reasonably small ensembles (especially when they are accompanied with so-called localization techniques). The stochastic framework presented here relies on location uncertainty principles that model the effects of the model errors on the large-scale flow components. The experiments carried out on the surface quasi-geostrophic model with the localized square-root filter demonstrate two significant improvements compared with the deterministic framework. First, as the uncertainty is a priori built into the model through the stochastic parametrization, there is no need for ad hoc variance inflation or perturbation of the initial condition. Second, it yields better mean-square-error results than the deterministic ones.

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Deciphering the Role of Small-Scale Inhomogeneity on Geophysical Flow Structuration: A Stochastic Approach

Cited by 35 publications

References 52 publications

Stochastic representation of mesoscale eddy effects in coarse-resolution barotropic models

Stochastic representation of mesoscale eddy effects in coarse-resolution barotropic models

Stochastic Modelling of Turbulent Flows for Numerical Simulations

Stochastic parametrization: An alternative to inflation in ensemble Kalman filters

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