Wirosoetisno, D. (2015) 'Navier-Stokes equations on a rapidly rotating sphere.', Discrete and continuous dynamical systems : series B., 20 (4). pp. 1251-1259.
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.
|Full text:||(AM) Accepted Manuscript|
Download PDF (177Kb)
|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|
Save or Share this output
|Look up in GoogleScholar|