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Co-rotating vortices with N fold symmetry for the inviscid surface quasi-geostrophic equation
TLDR
In this article, a variational construction of special solutions to the generalized surface quasi-geostrophic equations is provided, which take the form of N vortex patches with N-fold symmetry, which are steady in a uniformly rotating frame.Abstract:
We provide a variational construction of special solutions to the generalized surface quasi-geostrophic equations. These solutions take the form of N vortex patches with N-fold symmetry , which are steady in a uniformly rotating frame. Moreover, we investigate their asymptotic properties when the size of the corresponding patches vanishes. In this limit, we prove these solutions to be a desingularization of N Dirac masses with the same intensity, located on the N vertices of a regular polygon rotating at a constant angular velocity.read more
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Existence and regularity of co-rotating and traveling-wave vortex solutions for the generalized SQG equation
TL;DR: By studying the linearization of contour dynamics equation and using implicit function theorem, this paper proved the existence of co-rotating and traveling-wave vortex solutions for the gSQG equation, which extends the result of Hmidi and Mateu [28] to α ∈ [ 1, 2 ].
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Vortex collapses for the Euler and Quasi-Geostrophic Models
TL;DR: In this article, the trajectories for Euler and quasi-geostrophic vortices related to the non-neutral cluster hypothesis were studied and a convergence result was proved for the Euler point-vortex model.
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Multipole vortex patch equilibria for active scalar equations
Zineb Hassainia,Miles H. Wheeler +1 more
TL;DR: In this article, a general configuration of finitely many point vortices, in a state of uniform rotation or translation with Newtonian interaction or generalized surface quasi-geostrophic interactions, can be desingularized into a steady configuration of vortex patches.
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Existence and regularity of co-rotating and travelling global solutions for the generalized SQG equation
TL;DR: By studying the linearization of contour dynamics equation and using implicit function theorem, this article proved the existence of co-rotating and travelling global solutions for the gSQG equation, which extends the result of Hmidi and Mateu \cite{HM} to $\alpha\in[1,2]$.
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Existence of co-rotating and travelling vortex patches with doubly connected components for active scalar equations
TL;DR: By applying implicit function theorem on contour dynamics, the authors proved the existence of co-rotating and travelling patch solutions for both Euler and the generalized surface quasi-geostrophic equation.
References
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Book
Mathematical Methods of Classical Mechanics
TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
Mathematical methods of classical mechanics
TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
Book
Mathematical theory of incompressible non-viscous fluids
Carlo Marchioro,Mario Pulvirenti +1 more
TL;DR: In this article, the authors present an argument of large interest for physics, and applications in a rigorous logical and mathematical set-up, therefore avoiding cumbersome technicalities, which should fill a gap in the present literature.
Journal ArticleDOI
Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
TL;DR: In this paper, the formation of strong and potentially singular fronts in a two-dimensional quasigeostrophic active scalar is studied through the symbiotic interaction of mathematical theory and numerical experiments.
Journal ArticleDOI
Surface quasi-geostrophic dynamics
TL;DR: The dynamics of quasi-geostrophic flow with uniform potential vorticity reduces to the evolution of buoyancy, or potential temperature, on horizontal boundaries as discussed by the authors, but a different relationship between the flow and the advected scalar creates several distinctive features, such as an elliptical vortex, the start-up vortex shed by flow over a mountain, the instability of temperature filaments, the edge wave critical layer, and mixing in an overturning edge wave.
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