Stochastic forcing of quasi-geostrophic eddies

Müller, Peter

doi:10.1007/978-1-4612-2430-3_14

Cited by 14 publications

(9 citation statements)

References 17 publications

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“…There has been active recent research on stochastic approaches to geophysical flows [19,18,14,24,4] and numerical simulations of stochastically forced geophysical flows [25,26,5,6,27]. It is generally understood that random fluctuations can have delicate impact on geophysical fluid dynamics [19,14,25,26,10].…”

Section: Introductionmentioning

confidence: 99%

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Enstrophy dynamics of stochastically forced large-scale geophysical flows

Blömker

Duan

Wanner

2002

Journal of Mathematical Physics

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Section: Introductionmentioning

confidence: 99%

“…It is generally understood that random fluctuations can have delicate impact on geophysical fluid dynamics [19,14,25,26,10].…”

Section: Introductionmentioning

confidence: 99%

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Enstrophy dynamics of stochastically forced large-scale geophysical flows

Blömker

Duan

Wanner

2002

Journal of Mathematical Physics

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“…Stochastically forced QGE has been used to investigate various phenomena in geophysical flows [23,27,33,21,15,9]. Recently Salmon [32] introduced some generalized two-layer ocean flow models.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Dynamics of Two-Layer Geophysical Flows

2001

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Abstract. The two-layer quasigeostrophic flow model is an intermidiate system between the single-layer 2D barotropic flow model and the continuously stratified, 3D baroclinic flow model. This model is widely used to investigate basic mechanisms in geophysical flows, such as baroclinic effects, the Gulf Stream and subtropical gyres. The wind forcing acts only on the top layer. We consider the two-layer quasigeostrophic model under stochastic wind forcing. We first transformed this system into a coupled system of random partial differential equations and then show that the asymptotic probabilistic dynamics of this system depends only on the top fluid layer. Namely, in the probability sense and asymptotically, the dynamics of the two-layer quasigeostrophic fluid system is determinied by the top fluid layer, or, the bottom fluid layer is slaved by the top fluid layer. This conclusion is true provided that the Wiener process and the fluid parameters satisfy a certain condition. In particular, this latter condition is satisfied when the trace of the covariance operator of the Wiener process is controled by a certain upper bound, and the Ekman constant r is sufficiently large. Note that the generalized time derivative of the Wiener process models the fluctuating part of the wind stress forcing on the top fluid layer, and the Ekman constant r measures the rate for vorticity decay due to the friction in the bottom Ekman layer.

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“…The quasigeostrophic equation has been derived as an approximation of the rotating shallow water equations by the conventional asymptotic expansion in small Rossby number [14]. Recently, the randomly forced quasigeostrophic flow model has been used to study various phenomena in geophysical flows under uncertain wind forcing [5,10,11,12,16].…”

Section: Introductionmentioning

confidence: 99%

Ergodicity of stochastically forced large scale geophysical flows

Duan

Gołdys

2001

International Journal of Mathematics and Mathematical Sciences

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Abstract. We investigate the ergodicity of 2D large scale quasigeostrophic flows under random wind forcing. We show that the quasigeostrophic flows are ergodic under suitable conditions on the random forcing and on the fluid domain, and under no restrictions on viscosity, Ekman constant or Coriolis parameter. When these conditions are satisfied, then for any observable of the quasigeostrophic flows, its time average approximates the statistical ensemble average, as long as the time interval is sufficiently long.2000 Mathematics Subject Classification. 37A25, 60H15, 76D05, 86A05.

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Stochastic forcing of quasi-geostrophic eddies

Cited by 14 publications

References 17 publications

Enstrophy dynamics of stochastically forced large-scale geophysical flows

Enstrophy dynamics of stochastically forced large-scale geophysical flows

Probabilistic Dynamics of Two-Layer Geophysical Flows

Ergodicity of stochastically forced large scale geophysical flows

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