Related papers: Pointed vortex loops in ideal 2D fluids
We numerically investigate the flow structure of periodic steady water waves of fixed relative mass flux propagating on rotational flows with piece-wise constant vorticity. We show that for wave solutions along the global bifurcation…
Soft matters whose constituents are deformable are ubiquitous in nature especially in biological systems-including cells and their organelles-as well as in foams and emulsions. The capacity for deformation in these soft materials gives rise…
The methods of singular and de Rham homology and cohomology are reviewed to the extent that they are applicable to the structure and motion of vortices. In particular, they are first applied to the concept of integral invariants. After a…
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,…
The formalism of frozen-in vortex lines for two-dimensional (2D) flows in ideal incompressible electron magnetohydrodynamics (EMHD) is formulated. A localized approximation for nonlinear dynamics of two close sheets of the generalized…
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…
This chapter reviews the occurrence of quantised vortices in polariton fluids, primarily when polaritons are driven in the optical parametric oscillator (OPO) regime. We first review the OPO physics, together with both its analytical and…
This paper is concerned with steady vortex rings in an ideal fluid of uniform density, which are special global axi-symmetric solutions of the three-dimensional incompressible Euler equation. We systematically establish the existence,…
It is well known that the two-dimensional (2D) nonlinear Schr\"odinger equation (NLSE) with the cubic-quintic (CQ) nonlinearity supports a family of stable fundamental solitons, as well as solitary vortices (alias vortex rings), which are…
We answer affirmatively a question posed by Morita on homological stability of surface diffeomorphisms made discrete. In particular, we prove that $C^{\infty}$-diffeomorphisms and volume preserving diffeomorphisms of surfaces as family of…
The static and dynamic properties of vortices in dipolar Bose-Einstein condensates (dBECs) can be considerably modified relative to their nondipolar counterparts by the anisotropic and long-ranged nature of the dipole-dipole interaction.…
The point vortex model is an idealized model for describing the dynamics of many vortices with numerical efficiency, and has been shown to be powerful in modeling the dynamics of vortices in a superfluid. The model can be extended to…
We present an accurate Lagrangian method based on vortex particles, level-sets, and immersed boundary methods, for animating the interplay between two fluids and rigid solids. We show that a vortex method is a good choice for simulating…
Topological defects such as quantized vortices are one of the most striking manifestations of the superfluid nature of Bose-Einstein condensates and typical examples of quantum mechanical phenomena on a macroscopic scale. Here we…
We study the Euler equations on a rotating unit sphere, focusing on the dynamics of vortex caps. Leveraging the $L^1$-stability of monotone, longitude-independent profiles, we demonstrate that certain ill-prepared initial data within the…
Waves with constant vorticity and electrohydrodynamics flows are two topics in fluid dynamics that have attracted much attention from scientists for both the mathematical challenge and their industrial applications. The coupling of electric…
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…
Quantised vortices are remarkable manifestations on a macroscopic scale of the coherent nature of quantum fluids, and the study of their properties is of fundamental importance for the understanding of this peculiar state of matter.…
In this paper, we study two-dimensional steady incompressible Euler flows in which the vorticity is sharply concentrated in a finite number of regions of small diameter in a bounded domain. Mathematical analysis of such flows is an…
We study the Riemannian geometry of 3D axisymmetric ideal fluids. We prove that the $L^2$ exponential map on the group of volume-preserving diffeomorphisms of a $3$-manifold is Fredholm along axisymmetric flows with sufficiently small…