Related papers: Global time evolution of concentrated vortex rings
The evolution of a localized vortex in stably stratified flow, within the Boussinesq approximation, is analyzed using the fluid impulse concept. The set of equations describing the temporal development of the fluid impulse has an…
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,…
In this paper, we are concerned with nonlinear desingularization of steady vortex rings of three-dimensional incompressible Euler fluids. We focus on the case when the vorticity function has a simple discontinuity, which corresponding to a…
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…
We study numerically the behavior of a single quantized vortex in a rotating cylinder. We study in particular the spiraling motion of a vortex in a cylinder that is parallel to the rotation axis. We determine the asymptotic form of the…
We study stability of a spherical vortex introduced by M. Hill in 1894, which is an explicit solution of the three-dimensional incompressible Euler equations. The flow is axi-symmetric with no swirl, the vortex core is simply a ball sliding…
In the present work, motivated by numerous recent experimental developments we revisit the dynamics of a single vortex ring in anisotropic harmonic traps. At the theoretical level, we start from a general Lagrangian dynamically capturing…
The formation of a vortex ring from a piston/nozzle apparatus depends on the nozzle exit's shape. Here we study the formation mechanism and the evolution of asymmetrical rings from notched nozzles using direct numerical simulations. Three…
A classical problem in fluid mechanics is the motion of an axisymmetric vortex sheet evolving under the action of surface tension, surrounded by an inviscid fluid. Lagrangian descriptions of these dynamics are well-known, involving complex…
We consider axisymmetric incompressible inviscid flows without swirl in $\mathbb{R}^3$, under the assumption that the axial vorticity is non-positive in the upper half space and odd in the last coordinate, which corresponds to the flow…
We study the vortex dynamics in an evolutive flow. We carry out the statistical analysis of the resulting time series by means of the joint use of a compression and an entropy diffusion method. This approach to complexity makes it possible…
We consider the Euler equations in ${\mathbb R}^3$ expressed in vorticity form. A classical question that goes back to Helmholtz is to describe the evolution of solutions with a high concentration around a curve. The work of Da Rios in 1906…
The evolution of highly concentrated vorticity around rings in the three-dimensional axisymmetric Euler equations is studied in a regime for which the leapfrogging dynamics predicted by Helmholtz is expected to occur. We provide in this…
Vortex rings have the ability to transport fluid over long distances. They are usually produced by ejecting a volume of fluid through a circular orifice or nozzle. When the volume and velocity of the ejected fluid are known, the vortex'…
A self-similar solution for time evolution of quasi-spherical, self-gravitating accretion flows is obtained under the assumption that the generated heat by viscosity is retained in the flow. The solutions are parameterized by the ratio of…
We present an experimental study of the saturated non-linear dynamics of an inertial wave attractor in an axisymmetric geometrical setting. The experiments are carried out in a rotating ring-shaped fluid domain delimited by two vertical…
We study the Boussinesq approximation for rapidly rotating stably-stratified fluids in a three dimensional infinite layer with either stress-free or periodic boundary conditions in the vertical direction. For initial conditions satisfying a…
We consider incompressible Euler equations in any dimension $ d\geq3 $ imposing axisymmetric symmetry without swirl. While the global regularity of smooth flows in this setting has been well-known in $ d=3 $, the same question in higher…
In this paper we study the evolution of a small rigid body in a viscous incompressible fluid, in particular we show that a small particle is not accelerated by the fluid in the limit when its size converges to zero under a lower bound on…
We consider the evolution and dissipation of vortex rings in a condensate at non-zero temperature, in the context of the classical field approximation, based on the defocusing nonlinear Schr\"odinger equation. The temperature in such a…