Related papers: Exact solution to a nearly parallel vortex filamen…
The statistical mechanics of nearly parallel vortex filaments confined in the unbounded plane by angular momentum, first studied by Lions and Majda (2000), is investigated using a mean-field approximation to interaction and a spherical…
We investigate the occurrence of collisions in the evolution of vortex filaments through a system introduced by Klein, Majda and Damodaran [KMD95] and Zakharov [Z88,Z99]. We first establish rigorously the existence of a pair of almost…
Klein, Majda, and Damodaran have previously developed a formalized asymptotic motion law describing the evolution of nearly parallel vortex filaments within the framework of the three-dimensional Euler equations for incompressible fluids.…
Geophysical research has focused on flows, such as ocean currents, as two dimensional. Two dimensional point or blob vortex models have the advantage of having a Hamiltonian, whereas 3D vortex filament or tube systems do not necessarily…
Entangled vortex filaments are essential to turbulence, serving as coherent structures that govern nonlinear fluid dynamics and support the reconstruction of fluid fields to reveal statistical properties. This study introduces an quantum…
This paper gives an analysis of the movement of n+1 almost parallel filaments or vortices. Starting from a polygonal equilibrium of n vortices with equal circulation and one vortex at the center of the polygon, we find bifurcation of…
We introduce a framework to study the occurrence of vortex filament concentration in $3D$ Ginzburg-Landau theory. We derive a functional that describes the free-energy of a collection of nearly-parallel quantized vortex filaments in a…
In this study, we propose a new approach to describing certain macroscopic objects that can arise in a quantum fluid. These objects are formed by means of quantum entanglement from the circular-shaped mesoscale and microscale vortices, and…
We consider the classical point vortex model in the mean-field scaling regime, in which the velocity field experienced by a single point vortex is proportional to the average of the velocity fields generated by the remaining point vortices.…
Vortex filament model has become a standard and powerful tool to visualize the motion of quantized vortices in helium superfluids. In this article, we present an overview of the method and highlight its impact in aiding our understanding of…
In this proceedings article we shall survey a series of results on the stability of self-similar solutions of the vortex filament equation. This equation is a geometric flow for curves in $\mathbb R^3$ and it is used as a model for the…
We study the topology of quasiperiodic solutions of the vortex filament equation in a neighborhood of multiply covered circles. We construct these solutions by means of a sequence of isoperiodic deformations, at each step of which a real…
For the class of quasi-periodic solutions of the vortex filament equation, we study connections between the algebro-geometric data used for their explicit construction and the geometry of the evolving curves. We give a complete description…
Non-linear simulations of filament propagation in a realistic MAST SOL flux tube geometry using the BOUT++ fluid modelling framework show an isolation of the dynamics of the filament in the divertor region from the midplane region due to…
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 investigate exact nonlinear waves on surfaces locally approximating the rotating sphere for two-dimensional inviscid incompressible flow. Our first system corresponds to a beta-plane approximation at the equator and the second to a gamma…
The $n+1$ vortex filament problem has explicit solutions consisting of $n$ parallel filaments of equal circulation in the form of nested polygons uniformly rotating around a central filament which has circulation of opposite sign. We show…
We consider the Schr\"odinger system with Newton-type interactions that was derived by R. Klein, A. Majda and K. Damodaran [18] to modelize the dynamics of N nearly parallel vortex filaments in a 3-dimensional homogeneous incompressible…
Densely arranged optical vortices are natural solutions of high-symmetry Bloch modes in photonic crystals. However, strict symmetry constraints limit the potential spatial configurations of nearfield vortices, restricting the control over…
Quasiclassical approximation in the intrinsic description of the vortex filament dynamics is discussed. Within this approximation the governing equations are given by elliptic system of quasi-linear PDEs of the first order. Dispersionless…