Using the method of matched asymptotic expansion we construct the mobifity relation describing the vortex dynamics in the conservative Ginzburg-Landau equation with a spatially varying supercriticality parameter. For a particular case of a circularly symmetric supercriticality profile, we present the equations of vortex dynamics in a Hamiltonian form, and demonstrate the dynamic confinement of ...

We present a method for numerically building a vortex knot state in the superfluid wave function of a Bose-Einstein condensate. We integrate in time the governing Gross-Pitaevskii equation to determine evolution and shape preservation of the two (topologically) simplest vortex knots which can be wrapped over a torus. We find that the velocity of a vortex knot depends on the ratio of poloidal an...

The vortex method is applied to the calculation of a decaying homogeneous isotropic turbulence of Reλ = 25, 50 and the results are compared with a spectral method calculation. Vortex method calculations were accelerated by the use of a fast multipole method for periodic boundary conditions. The core spreading method and particle strength exchange were selected as the viscous diffusion scheme. T...

We propose a method for the stabilization of a stack of parallel vortex rings in a Bose–Einstein condensate. The method makes use of a ‘hollow’ laser beam containing an optical vortex. Using realistic experimental parameters we demonstrate numerically that our method can stabilize up to nine vortex rings. Furthermore we point out that the condensate flow through the tunnel formed by the core of...

Here the hollow vortex Gaussian beam is described by the exact solution of the Maxwell equations. By means of the method of the vectorial angular spectrum, analytical expressions of the electromagnetic fields of a hollow vortex Gaussian beam propagating in free space are derived. By using the electromagnetic fields of a hollow vortex Gaussian beam beyond the paraxial approximation, one can calc...

This article reviews some recent simulations of vortex sheet roll-up using the vortex blob method. In planar and axisymmetric flow, the roll-up is initially smooth but irregular small-scale features develop later in time due to the onset of chaos. A numerically generated Poincaré section shows that the vortex sheet flow resembles a chaotic Hamiltonian system with resonance bands and a heterocli...

A grid free method for approximating incompressible boundary layers is introduced. The computational elements are segments of vortex sheets. The method is related to the earlier vortex method; simplicity is achieved at the cost of replacing the Navier-Stokes equations by the Prandtl boundary layer equations. A new method for generating vorticity at boundaries is also presented; it can be used w...

In the present paper a description of a problem of point vortices on a plane and a sphere in the " internal " variables is discussed. The Hamiltonian equations of motion of vortices on a plane are built on the Lie–Poisson algebras, and in the case of vortices on a sphere on the quadratic Jacobi algebras. The last ones are obtained by deformation of the corresponding linear algebras. Some partia...