Stuart-type polar vortices on a rotating sphere

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Title: Stuart-type polar vortices on a rotating sphere
Authors: Constantin, A
Crowdy, D
Krishnamurthy, V
Wheeler, M
Item Type: Journal Article
Abstract: Stuart vortices are among the few known smooth explicit solu-tions of the planar Euler equations with a nonlinear vorticity, and they can beadapted to model inviscid flow on the surface of a fixed sphere. By means ofaperturbativeapproachweshowthatthemethodusedtoinvestigateStuartvortices on a fixed sphere provides insight into the dynamics of the large-scalezonal flows on a rotating sphere that model the background flow of polar vor-tices. Our approach takes advantage of the fact that while a sphere is spinningaround its polar axis, every point on the sphere has the same angular velocitybut its tangential velocity is proportional to the distance from the polar axisof rotation, so that points move fastest at the Equator and slower as we gotowards the poles, both of which remain fixed.
Issue Date: Jan-2021
Date of Acceptance: 13-May-2020
DOI: 10.3934/dcds.2020263
ISSN: 1078-0947
Publisher: American Institute of Mathematical Sciences
Start Page: 201
End Page: 215
Journal / Book Title: Discrete and Continuous Dynamical Systems Series A
Volume: 41
Issue: 1
Copyright Statement: © 2021 American Institute of Mathematical Sciences
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Euler equation
rotating frame
stereographic projection
nonlinear elliptic equation
sub- and super-solutions
Applied Mathematics
0101 Pure Mathematics
0102 Applied Mathematics
Publication Status: Published
Online Publication Date: 2021-01
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences