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| Resseguier, Valentin; Memin, Etienne; Heitz, Dominique; Chapron, Bertrand. |
| We present here a new stochastic modelling approach in the constitution of fluid flow reduced-order models. This framework introduces a spatially inhomogeneous random field to represent the unresolved small-scale velocity component. Such a decomposition of the velocity in terms of a smooth large-scale velocity component and a rough, highly oscillating component gives rise, without any supplementary assumption, to a large-scale flow dynamics that includes a modified advection term together with an inhomogeneous diffusion term. Both of those terms, related respectively to turbophoresis and mixing effects, depend on the variance of the unresolved small-scale velocity component. They bring an explicit subgrid term to the reduced system which enables us to take... |
| Tipo: Text |
Palavras-chave: Low-dimensional models; Turbulence modelling; Turbulent mixing. |
| Ano: 2017 |
URL: http://archimer.ifremer.fr/doc/00396/50698/53726.pdf |
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| Resseguier, Valentin; Memin, Etienne; Chapron, Bertrand. |
| In large-scale Fluids Dynamics systems, the velocity lives in a broad range of scales. To be able to simulate its large-scale component, the flow can be de- composed into a finite variation process, which represents a smooth large-scale velocity component, and a martingale part, associated to the highly oscillating small-scale velocities. Within this general framework, a stochastic representation of the Navier-Stokes equations can be derived, based on physical conservation laws. In this equation, a diffusive sub-grid tensor appears naturally and gener- alizes classical sub-grid tensors. Here, a dimensionally reduced large-scale simulation is performed. A Galerkin projection of our Navier-Stokes equation is done on a Proper Orthogonal De- composition basis.... |
| Tipo: Text |
Palavras-chave: Stochastic calculus; Uid dynamics; Large eddy simulation; Proper Orthogonal Decomposition; Reduced order model; Uncertainty quantification. |
| Ano: 2015 |
URL: http://archimer.ifremer.fr/doc/00320/43080/42607.pdf |
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| Resseguier, Valentin; Memin, E.; Chapron, Bertrand. |
| A stochastic flow representation is considered with the Eulerian velocity decomposed between a smooth large scale component and a rough small-scale turbulent component. The latter is specified as a random field uncorrelated in time. Subsequently, the material derivative is modified and leads to a stochastic version of the material derivative to include a drift correction, an inhomogeneous and anisotropic diffusion, and a multiplicative noise. As derived, this stochastic transport exhibits a remarkable energy conservation property for any realizations. As demonstrated, this pivotal operator further provides elegant means to derive stochastic formulations of classical representations of geophysical flow dynamics. |
| Tipo: Text |
Palavras-chave: Stochastic flows; Uncertainty quantification; Ensemble forecasts; Upper ocean dynamics. |
| Ano: 2017 |
URL: http://archimer.ifremer.fr/doc/00385/49598/51086.pdf |
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| Resseguier, Valentin; Memin, E.; Chapron, Bertrand. |
| Models under location uncertainty are derived assuming that a component of the velocity is uncorrelated in time. The material derivative is accordingly modified to include an advection correction, inhomogeneous and anisotropic diffusion terms and a multiplicative noise contribution. In this paper, simplified geophysical dynamics are derived from a Boussinesq model under location uncertainty. Invoking usual scaling approximations and a moderate influence of the subgrid terms, stochastic formulations are obtained for the stratified Quasi-Geostrophy and the Surface Quasi-Geostrophy models. Based on numerical simulations, benefits of the proposed stochastic formalism are demonstrated. A single realization of models under location uncertainty can restore... |
| Tipo: Text |
Palavras-chave: Stochastic sub-grid parameterization; Uncertainty quantification; Ensemble forecasts. |
| Ano: 2017 |
URL: http://archimer.ifremer.fr/doc/00385/49599/51087.pdf |
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| Resseguier, Valentin; Memin, E.; Chapron, Bertrand. |
| Models under location uncertainty are derived assuming that a component of the velocity is uncorrelated in time. The material derivative is accordingly modified to include an advection correction, inhomogeneous and anisotropic diffusion terms and a multiplicative noise contribution. This change can be consistently applied to all fluid dynamics evolution laws. This paper continues to explore benefits of this framework and consequences of specific scaling assumptions. Starting from a Boussinesq model under location uncertainty, a model is developed to describe a mesoscale flow subject to a strong underlying submesoscale activity. Specifically, turbulent diffusion and rotation effects have similar orders of magnitude. As obtained, the geostrophic balance is... |
| Tipo: Text |
Palavras-chave: Stochastic subgrid tensor; Uncertainty quantification; Upper ocean dynamics. |
| Ano: 2017 |
URL: http://archimer.ifremer.fr/doc/00385/49600/51088.pdf |
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| Chapron, Bertrand; Derian, P.; Memin, E.; Resseguier, Valentin. |
| 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... |
| Tipo: Text |
Palavras-chave: Large-scale flow modelling; Stochastic parametrization; Modelling under location uncertainty; Stochastic Lorenz model; Stochastic transport. |
| Ano: 2018 |
URL: https://archimer.ifremer.fr/doc/00429/54081/56227.pdf |
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