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Abstract
We study analytical and numerical aspects of the bifurcation diagram of
simply connected rotating vortex patch equilibria for the
quasi-geostrophic shallow-water (QGSW) equations. The QGSW equations are
a generalisation of the Euler equations and contain an additional
parameter, the Rossby deformation length ε−1,
which enters into the relation between the stream function and
(potential) vorticity. The Euler equations are recovered in the limit ε→0.
We prove, close to circular (Rankine) vortices, the persistence of the
bifurcation diagram for arbitrary Rossby deformation length. However we
show that the two-fold branch, corresponding to Kirchhoff ellipses for
the Euler equations, is never connected even for small values ε,
and indeed is split into a countable set of disjoint connected
branches. Accurate numerical calculations of the global structure of the
bifurcation diagram and of the limiting equilibrium states are also
presented to complement the mathematical analysis.
Original language | English |
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Pages (from-to) | 1853-1915 |
Number of pages | 63 |
Journal | Archive for Rational Mechanics and Analysis |
Volume | 231 |
Issue number | 3 |
Early online date | 12 Oct 2018 |
DOIs | |
Publication status | Published - Mar 2019 |
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Dive into the research topics of 'Imperfect bifurcation for the quasi-geostrophic shallow-water equations'. Together they form a unique fingerprint.Projects
- 1 Finished
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Geophysical Vortices: The Structure, stability and interaction of geophysical vortices
Reinaud, J. N. (PI), Dritschel, D. G. (CoI) & Scott, R. K. (CoI)
5/01/10 → 1/11/13
Project: Standard