Related papers: Vortex pairs and dipoles on closed surfaces

We examine the Euler equations within a simply-connected bounded domain. The dynamics of a single point vortex are governed by a Hamiltonian system, with most of its energy levels corresponding to time-periodic motion. We show that for the…

We extend our previous analysis of the motion of vortex lines [I. Bialynicki-Birula, Z. Bialynicka-Birula and C. Sliwa, Phys. Rev. A 61, 032110 (2000)] from linear to a nonlinear Schroedinger equation with harmonic forces. We also argue…

A general formulation is presented for studying the motion of buoyant vortices in a homogeneous ambient fluid. It extends the well-known Hamiltonian framework for interacting homogeneous point vortices to include buoyancy effects acting on…

We start by surveying the planar point vortex motion of the Euler equations in the whole plane, half-plane and quadrant. Then we go on to prove non-collision property of 2-vortex system by using the explicit form of orbits of 2-vortex…

The restricted three-vortex problem is investigated with one of the point vortices fixed in the plane. The motion of the free vortex having zero circulation is explored from a rotating frame of reference within which the free vortex with…

We investigate the collective dynamics of multivortex assemblies in a two dimensional (2D) toroidal fluid film of distinct curvature and topology. The incompressible and inviscid nature of the fluid allows a Hamiltonian description of the…

The study of superfluid and Berezinskii-Kosterlitz-Thouless phases in exciton-polaritons requires an understanding of vortex dynamics in a dissipative unconfined condensate. In this article we study the motion of dynamic vortex-antivortex…

The existence of a local curve of corotating and counter-rotating vortex pairs was proven by Hmidi and Mateu in via a desingularization of a pair of point vortices. In this paper, we construct a global continuation of these local curves.…

We study the motion of a single point vortex in simply and multiply connected polygonal domains. In case of multiply connected domains, the polygonal obstacles can be viewed as the cross-sections of 3D polygonal cylinders. First, we utilize…

In this paper, we study desingularization of vortices for the two-dimensional incompressible Euler equations in the full plane. We construct a family of steady vortex pairs for the Euler equations with a general vorticity function, which…

In this article, we first investigate the kinematics of specific geodesic flows on two dimensional media with constant curvature, by explicitly solving the evolution (Raychaudhuri) equations for the expansion, shear and rotation along the…

We study the dynamics of quantized superfluid vortices on axisymmetric compact surfaces with no holes, where the total vortex charge must vanish and the condition of irrotational flow forbids distributed vorticity. A conformal…

We develop a neutral vortex fluid theory on closed surfaces with zero genus. The theory describes collective dynamics of many well-separated quantum vortices in a superfluid confined on a closed surface. Comparing to the case on a plane,…

One field of fluid dynamics concerns the search for variational principles. So far, the Hamiltonian view and Riemannian geometry has been applied to find geodesics for hydrodynamic systems. Compared to Riemannian geometry sub-Riemannian…

The aim of this contribution is to make a connection between two recent results concerning the dynamics of vortices in incompressible planar flows. The first one is an asymptotic expansion, in the vanishing viscosity limit, of the solution…

We consider the problem of reconstructing a background potential from the dynamical behavior of vortex dipole. We prove that under suitable conditions, one can uniquely reconstruct a real-analytic potential by measuring the entrance and…

We give an exact quantitative solution for the motion of three vortices of any strength, which Poincar\'e showed to be integrable. The absolute motion of one vortex is generally biperiodic: in uniformly rotating axes, the motion is…

The dynamics of 2D pancake vortices in Josephson-coupled superconducting/normal - metal multilayers is considered within the time-dependent Ginzburg-Landau theory. For temperatures close to $T_{c}$ a viscous drag force acting on a moving 2D…

The general local, nondissipative equations of motion for a quantized vortex moving in an uncharged laboratory superfluid are derived from a relativistic, co-ordinate invariant framework, having vortices as its elementary objects in the…

For the model of a compressible barotropic fluid on a two dimensional rotating Riemmanian manifold we discuss a special class of smooth solutions having a form of a steady non-singular vortex moving with a bearing field. The model can be…