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Navier-Stokes equations on a rapidly rotating sphere.

Wirosoetisno, D. (2015) 'Navier-Stokes equations on a rapidly rotating sphere.', Discrete and continuous dynamical systems : series B., 20 (4). pp. 1251-1259.

Abstract

We extend our earlier β-plane results [al-Jaboori and Wirosoetisno, 2011, DCDS-B 16:687--701] to a rotating sphere. Specifically, we show that the solution of the Navier--Stokes equations on a sphere rotating with angular velocity 1/ϵ becomes zonal in the long time limit, in the sense that the non-zonal component of the energy becomes bounded by ϵM. Central to our proof is controlling the behaviour of the nonlinear term near resonances. We also show that the global attractor reduces to a single stable steady state when the rotation is fast enough.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.3934/dcdsb.2015.20.1251
Publisher statement:This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and continuous dynamical systems : series B following peer review. The definitive publisher-authenticated version Wirosoetisno, D (2015). Navier-Stokes equations on a rapidly rotating sphere. Discrete and Continuous Dynamical Systems - Series B 20(4): 1251-1259 is available online at: https://doi.org/10.3934/dcdsb.2015.20.1251
Date accepted:15 January 2015
Date deposited:13 September 2017
Date of first online publication:01 February 2015
Date first made open access:No date available

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