Related papers: Vortex patches choreography for active scalar equa…
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…
In the spirit of Prandtl's conjecture of 1926, for turbulence at high Reynolds number we present an analogy with the kinetic theory of gases, with dipoles made of quasi-rigid and 'dressed' vortex tubes as frictionless, incompressible but…
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…
The motion of two pairs of counter-rotating point vortices placed in a uniform flow past a circular cylinder is studied analytically and numerically. When the dynamics is restricted to the symmetric subspace---a case that can be realized…
It is well known that the Euler vortex patch in $\mathbb{R}^{2}$ will remain regular if it is regular enough initially. In bounded domains, the regularity theory for patch solutions is less complete. We study here the Euler vortex patch in…
We consider the motion of a vortex in an asymptotically homogeneous condensate bounded by a solid wall where the wave function of the condensate vanishes. For a vortex parallel to the wall, the motion is essentially equivalent to that…
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…
Vortex streets are periodic configurations of vortices propagating through an irrotational flow. In this paper, we study streets of hollow vortices, which are solutions to the free boundary $2$-d irrotational incompressible Euler equations.…
In this work we have found an exact solution for the problem of the movement of a dipole type point vortex in an area of fluid limited by a flat boundary. We also present a solution to the problem of dipole point vortex motion in a right…
We prove that for $\omega: \mathbb{R}^2 \to [0,1]$ sharing the same total vorticity and center of vorticity as the Rankine vortex, the $L^1$ deviation from the Rankine patch can be bounded by a function of the pseudo-energy deviation and…
Studies of particle motion in vortical flows have mainly focused on point-like particles, either inertial or self-propelled. This approximation assumes that the velocity field that surrounds the particle is linear. We consider an…
We study the dynamics of $N$ point vortices on a rotating sphere. The Hamiltonian system becomes infinite dimensional due to the non-uniform background vorticity coming from the Coriolis force. We prove that a relative equilibrium formed of…
By utilizing the AdS/CFT correspondence, we explore the dynamics of strongly coupled superfluid vortices in a disk with constant angular velocity. Each vortex in the vortex lattice is quantized with vorticity one from the direct inspection…
When a two-component Bose-Einstein condensate is placed into rotation, a lattice of vortices and cores appear. The geometry of this lattice (triangular or square) varies according to the rotational value and the intercomponent coupling…
We set up general equations of motion for point vortex systems on closed Riemannian surfaces, allowing for the case that the sum of vorticities is not zero and there hence must be counter-vorticity present. The dynamics of global…
We analyze the problem of quadrangulating a $n$-sided patch, each side at its boundary subdivided into a given number of edges, using a single irregular vertex (or none, when $n = 4$) that breaks the otherwise fully regular lattice. We…
Thin vortex tubes, with core sizes within the dissipation range, profuse in a homogeneous and isotropic turbulent flow. Their intersections with an arbitrary plane define, as a mathematical construct, a dilute gas of localized,…
The point vortex dynamics in background fields on surfaces is justified as an Euler-Arnold flow in the sense of de Rham currents. We formulate a current-valued solution of the Euler-Arnold equation with a regular-singular decomposition. For…
We consider massive vortices in binary condensates, where the immiscibility condition entails the trapping of the minority component in the vortex cores of the majority component. We study such vortices by means of a 2D point-like model,…
We study a special kind of singular vorticities in ideal 2D fluids that combine features of point vortices and vortex sheets, namely pointed vortex loops. We focus on the coadjoint orbits of the area-preserving diffeomorphism group of…