Navier-Stokes equations on a rapidly rotating sphere

2013/08/05 by D. Wirosoetisno, Wirosoetisno, Djoko · 1 citation
Engineering · Mathematics · #35B40 #35B41 #35R01 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1308.1045

openalex publication_date 2013/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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. We also show that the global attractor reduces to a single stable steady state when the rotation is fast enough.

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• Difference estimate for weak solutions to the Navier-Stokes equations in a thin spherical shell and on the unit sphere

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