Related papers: Leapfrogging vortex rings as scaling limit of Eule…
We study the time evolution of a viscous incompressible fluid with axial symmetry without swirl, when the initial vorticity is very concentrated in $N$ disjoint rings. We show that in a suitable joint limit, in which both the thickness of…
The dynamics of a circular thin vortex ring and a sphere moving along the symmetry axis of the ring in an inviscid incompressible fluid is studied on the basis of Euler's equations of motion. The equations of motion for position and radius…
In this paper, we study nonlinear desingularization of steady vortex rings of three-dimensional incompressible Euler flows. We construct a family of steady vortex rings (with and without swirl) which constitutes a desingularization of the…
We study desingularization of steady vortex rings in three-dimensional axisymmetric incompressible Euler fluids with swirl. Using the variational method, we construct a two-parameter family of steady vortex rings, which constitute a…
In the present note, we solved numerically the viscous vorticity equation of the initial-boundary value problem describing the classic Helmholtz phenomena of vortex interaction. In the leapfrogging of vortex pairs, we demonstrate the fact…
The fluid motion produced by a periodic array of identical, axisymmetric, thin-cored vortex rings is investigated. It is well known that such an array moves uniformly without change of shape or form in the direction of the central axis of…
A simple - yet plausible - model for B-type vortex breakdown flows is postulated; one that is based on the immersion of a pair of slender coaxial vortex rings in a swirling flow of an ideal fluid rotating around the axis of symmetry of the…
It is well-known that the dynamics of vortices in an ideal incompressible two-dimensional fluid contained in a bounded not necessarily simply connected smooth domain is described by the Kirchhoff--Routh point vortex system. In this paper,…
We treat string propagation and interaction in the presence of a background Neveu-Schwarz three-form field strength, suitable for describing vortex rings in a superfluid or low-viscosity normal fluid. A circular vortex ring exhibits…
We deal with the incompressible Navier-Stokes equations, in two and three dimensions, when some vortex patches are prescribed as initial data i.e. when there is an internal boundary across which the vorticity is discontinuous. We show…
The leapfrogging motion of smoke rings is a three dimensional version of the motion that in two dimensions leads to exotic exchange statistics. The statistical phase factor can be computed using the hydrodynamical Euler equation, which is a…
The leapfrogging of coaxial vortex rings is a famous effect which has been noticed since the times of Helmholtz. Recent advances in ultra-cold atomic gases show that the effect can now be studied in quantum fluids. The strong confinement…
The dynamics of a small rigid spherical particle in an unbounded pulsating vortex is considered, keeping constant the particle Stokes number St and varying the particle-to-fluid density ratio $\varrho$ and the pulsation frequency of the…
We consider the two-dimensional incompressible Euler equation \[\begin{cases} \partial_t \omega + u\cdot \nabla \omega=0 \\ \omega(0,x)=\omega_0(x). \end{cases}\] We are interested in the cases when the initial vorticity has the form…
For axisymmetric flows without swirl and compactly supported initial vorticity, we prove the upper bound of $t^{4/3}$ for the growth of the vorticity maximum, which was conjectured by Childress [Phys. D, 2008] and supported by numerical…
An evolution of a spherical region, subjected to uniform buoyancy force, is investigated. Incompressibility and axial symmetry are assumed, together with a buoyancy discontinuity at the boundary. The boundary turns into a vortex sheet and…
We establish the stability of a pair of Hill's spherical vortices moving away from each other in 3D incompressible axisymmetric Euler equations without swirl. Each vortex in the pair propagates away from its odd-symmetric counterpart, while…
The incompressible Navier-Stokes equations in R^3 are shown to admit a unique axisymmetric solution without swirl if the initial vorticity is a circular vortex filament with arbitrarily large circulation Reynolds number. The emphasis is on…
Turbulent flows of incompressible liquid in two dimensions are comprised of dense systems of vortices. Such system of vortices can be treated as a fluid and itself could be described in terms of hydrodynamics. We develop the hydrodynamics…
Irrotational relativistic vortex configurations in uniform subsonic motion with respect to a surrounding perfect fluid are analysed for the purpose of application to superfluid layers in neutron stars. Asymptotic solutions are found by…