Navier-Stokes equations on a rapidly rotating sphere

Wirosoetisno, D

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.

Citation

Wirosoetisno, D. (2015). Navier-Stokes equations on a rapidly rotating sphere. Discrete and Continuous Dynamical Systems - Series B, 20(4), 1251-1259. https://doi.org/10.3934/dcdsb.2015.20.1251

• Journal Article Type: Article
• Acceptance Date: Jan 15, 2015
• Online Publication Date: Feb 1, 2015
• Publication Date: Feb 1, 2015
• Deposit Date: Sep 29, 2016
• Publicly Available Date: Sep 13, 2017
• Journal: Discrete and Continuous Dynamical Systems - Series B
• Print ISSN: 1531-3492
• Electronic ISSN: 1553-524X
• Publisher: American Institute of Mathematical Sciences (AIMS)
• Peer Reviewed: Peer Reviewed
• Volume: 20
• Issue: 4
• Pages: 1251-1259
• DOI: https://doi.org/10.3934/dcdsb.2015.20.1251