Enstrophy dynamics of stochastically forced large-scale geophysical flows

Blömker, Dirk; Duan, Jinqiao; Wanner, Thomas

doi:10.1063/1.1459755

Cited by 4 publications

(3 citation statements)

References 26 publications

(50 reference statements)

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“…Furthermore, we show that for t → 0 the linear regime dominates. In [3] also H"older-continuity for the mean energy was shown for a quasigeostrophic model. We conclude this section by a qualitative discussion on upper bounds for the energy using additive and multiplicative trace-class noise.…”

Section: Nonlinear Theorymentioning

confidence: 94%

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Predictability of the Burgers Dynamics Under Model Uncertainty

Blömker

Duan

2007

Stochastic Differential Equations: Theory and Applications

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Complex systems may be subject to various uncertainties. A great effort has been concentrated on predicting the dynamics under uncertainty in initial conditions. In the present work, we consider the well-known Burgers equation with random boundary forcing or with random body forcing. Our goal is to attempt to understand the stochastic Burgers dynamics by predicting or estimating the solution processes in various diagnostic metrics, such as mean length scale, correlation function and mean energy. First, for the linearized model, we observe that the important statistical quantities like mean energy or correlation functions are the same for the two types of random forcing, even though the solutions behave very differently. Second, for the full nonlinear model, we estimate the mean energy for various types of random body forcing, highlighting the different impact on the overall dynamics of space-time white noises, trace class white-in-time and colored-in-space noises, point noises, additive noises or multiplicative noises.

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Section: Nonlinear Theorymentioning

confidence: 94%

“…Here we rely on a much simpler tool, which can also be applied to other equations. See for instance [3] for a quasigeostrophic model, where our analysis would apply, too.…”

Section: Body Forcing -Mean Energy Boundsmentioning

confidence: 99%

Predictability of the Burgers Dynamics Under Model Uncertainty

Blömker

Duan

2007

Stochastic Differential Equations: Theory and Applications

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“…For other ocean models, the reader is referred to [4,5,[10][11][12][13][14] for the mathematical study, and to [15,16,21,22] for the physical background, among others.…”

Section: Introductionmentioning

confidence: 99%

Exponential stability of the multi-layer quasi-geostrophic ocean model with delays

Wan

Duan

2009

Nonlinear Analysis: Theory, Methods & Applications

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Stochastic parameterization for large eddy simulation of geophysical flows

Duan

Nadiga

2007

Proc. Amer. Math. Soc.

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Abstract. Recently, stochastic, as opposed to deterministic, parameterizations are being investigated to model the effects of unresolved subgrid scales (SGS) in large eddy simulations (LES) of geophysical flows. We analyse such a stochastic approach in the barotropic vorticity equation to show that (i) if the stochastic parameterization approximates the actual SGS stresses, then the solution of the stochastic LES approximates the "true" solution at appropriate scale sizes; and that (ii) when the filter scale size approaches zero, the solution of the stochastic LES approaches the true solution.

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Enstrophy dynamics of stochastically forced large-scale geophysical flows

Cited by 4 publications

References 26 publications

Predictability of the Burgers Dynamics Under Model Uncertainty

Predictability of the Burgers Dynamics Under Model Uncertainty

Exponential stability of the multi-layer quasi-geostrophic ocean model with delays

Stochastic parameterization for large eddy simulation of geophysical flows

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