Results 1 to 10 of about 12,014 (293)
Equations of motion for weakly compressible point vortices [PDF]
Philosophical Transactions Series A, Mathematical, Physical, and Engineering Sciences, 2022 Equations of motion for compressible point vortices in the plane are obtained in the limit of small Mach number, M , using a Rayleigh–Jansen expansion and the method of Matched Asymptotic Expansions.
Stefan Llewellyn Smith, Tianyi Chu
exaly +6 more sources
Equilibria and stability of four point vortices on a sphere [PDF]
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2020 This paper discusses the problem of finding the equilibrium positions of four point vortices, of generally unequal circulations, on the surface of a sphere. A random search method is developed which uses a modification of the linearized equations to converge on distinct equilibria.
David Dritschel
exaly +7 more sources
The motion of point vortices on closed surfaces [PDF]
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2015 We develop a mathematical framework for the dynamics of a set of point vortices on a class of differentiable surfaces conformal to the unit sphere. When the sum of the vortex circulations is non-zero, a compensating uniform vorticity field is required to
David Dritschel
exaly +4 more sources
Motion of buoyant point vortices [PDF]
Physical Review Fluids, 2020 A general Hamiltonian description for the trajectories of any number of interacting buoyant vortices in a homogeneous ambient fluid is presented. It constitutes an idealized description of coherent vortex structures in environmental flows where buoyancy forces are relevant for the evolution of such structures.
Jeffrey R. Carpenter, Anirban Guha
core +7 more sources
Generalised point vortices on a plane
Physics Letters B, 2022 A three–vortex system on a plane is known to be minimally superintegrable in the Liouville sense. In this work, integrable generalisations of the three–vortex planar model, which involve root vectors of simple Lie algebras, are proposed. It is shown that
Anton Galajinsky
doaj +5 more sources
Hölder regularity for collapses of point-vortices [PDF]
Nonlinearity, 2023 Abstract The first part of this article studies the collapses of point-vortices for the Euler equation in the plane and for surface quasi-geostrophic equations in the general setting of α models. In these models the kernel of the Biot–Savart law is a power function of exponent
Martin Donati, Ludovic Godard-Cadillac
openaire +3 more sources
Pensive Billiards, Point Vortices, And The Silver Ratio
Forum of Mathematics, SigmaWe define a new class of plane billiards – the “pensive billiard” – in which the billiard ball travels along the boundary for some distance depending on the incidence angle before reflecting, while preserving the billiard rule of equality of the angles ...
Theodore Drivas +2 more
doaj +3 more sources
Point vortices on the sphere: Stability of symmetric relative equilibria [PDF]
Journal of Geometric Mechanics, 2011 We describe the linear and nonlinear stability and instability of certain symmetric configurations of point vortices on the sphere forming relative equilibria. These configurations consist of one or two rings, and a ring with one or two polar vortices.
James Montaldi
exaly +5 more sources
Collapse of n Point Vortices, Formation of the Vortex Sheets and Transport of Passive Markers
Energies, 2021 In this paper, the motion of the n-vortex system as it collapses to a point in finite time is studied. The motion of vortices is described by the set of ordinary differential equations that we are able to solve analytically.
Henryk Kudela
doaj +1 more source
On the Effects of Circulation around a Circle on the Stability of a Thomson Vortex N-gon
Mathematics, 2020 The stability problem of the stationary rotation of N identical point vortices is considered. The vortices are located on a circle of radius R 0 at the vertices of a regular N-gon outside a circle of radius R.
Leonid Kurakin, Irina Ostrovskaya
doaj +1 more source