scholarly journals Motion of a Particle Immersed in a Two Dimensional Incompressible Perfect Fluid and Point Vortex Dynamics

2017 ◽  
pp. 139-216 ◽  
Author(s):  
F. Sueur
Keyword(s):  
Perfect Fluid ◽  
Vortex Dynamics ◽  
Point Vortex ◽  
Two Dimensional

scholarly journals Integrability of Point-Vortex Dynamics via Symplectic Reduction: A Survey

2020 ◽  
Author(s):  
Klas Modin ◽  
Milo Viviani
Keyword(s):  
Euler Equations ◽  
Vortex Dynamics ◽  
Point Vortex ◽  
Point Vortices ◽  
Symplectic Reduction ◽  
Dimensional Manifold ◽  
Two Dimensional ◽  
Unified Framework ◽  
Long Time ◽  
2D Euler Equations

Abstract Point-vortex dynamics describe idealized, non-smooth solutions to the incompressible Euler equations on two-dimensional manifolds. Integrability results for few point-vortices on various domains is a vivid topic, with many results and techniques scattered in the literature. Here, we give a unified framework for proving integrability results for $$N=2$$ N = 2 , 3, or 4 point-vortices (and also more general Hamiltonian systems), based on symplectic reduction theory. The approach works on any two-dimensional manifold with a symmetry group; we illustrate it on the sphere, the plane, the hyperbolic plane, and the flat torus. A systematic study of integrability is prompted by advances in two-dimensional turbulence, bridging the long-time behaviour of 2D Euler equations with questions of point-vortex integrability. A gallery of solutions is given in the appendix.

Analogous formulation of electrodynamics and two-dimensional fluid dynamics

2014 ◽  
Vol 761 ◽  
Author(s):  
Rick Salmon
Keyword(s):  
Fluid Dynamics ◽  
Charge Density ◽  
Compressible Flow ◽  
Vortex Dynamics ◽  
Point Vortex ◽  
Point Vortices ◽  
Classical Electrodynamics ◽  
Two Dimensional ◽  
Electric Charge Density ◽  
Limiting Case

AbstractA single, simply stated approximation transforms the equations for a two-dimensional perfect fluid into a form that is closely analogous to Maxwell’s equations in classical electrodynamics. All the fluid conservation laws are retained in some form. Waves in the fluid interact only with vorticity and not with themselves. The vorticity is analogous to electric charge density, and point vortices are the analogues of point charges. The dynamics is equivalent to an action principle in which a set of fields and the locations of the point vortices are varied independently. We recover classical, incompressible, point vortex dynamics as a limiting case. Our full formulation represents the generalization of point vortex dynamics to the case of compressible flow.

Two-dimensional vortex dynamics in a stratified barotropic fluid

1996 ◽  
Vol 314 ◽  
pp. 139-161 ◽  
Author(s):  
Steve C. Arendt
Keyword(s):  
Gravitational Field ◽  
Vortex Dynamics ◽  
Point Vortex ◽  
The Self ◽  
Uniform Density ◽  
Hamiltonian Form ◽  
Two Dimensional ◽  
Barotropic Fluid ◽  
Isothermal Fluid ◽  
Uniform Fluid

We show that two-dimensional ‘point’ vortex dynamics in both a polytropic fluid of γ = 3/2 and an isothermal fluid stratified by a constant gravitational field can be written in Hamiltonian form. We find that the formulation admits only one constant of the motion in addition to the Hamiltonian, so that two vortices are the most for which the motion is generally integrable. We study in detail the two-vortex problem and find a rich collection of behaviour: closed trajectories analogous to the circular orbits of the uniform-fluid two-vortex problem, open trajectories for which the self-propelled vortices scatter off each other, and both unstable and stable steadily translating pairs of vortices. Comparison is made to the case of two vortices in a uniform-density fluid bounded by a wall.

A simple point vortex model for two‐dimensional decaying turbulence

1992 ◽  
Vol 4 (5) ◽  
pp. 1036-1039 ◽  
Author(s):  
R. Benzi ◽  
M. Colella ◽  
M. Briscolini ◽  
P. Santangelo
Keyword(s):  
Point Vortex ◽  
Two Dimensional ◽  
Simple Point ◽  
Vortex Model ◽  
Decaying Turbulence ◽  
Point Vortex Model

Two-dimensional vortex dynamics in decoupledYBa2Cu3O7/PrBa2Cu3O7superlattices

2003 ◽  
Vol 68 (2) ◽  
Author(s):  
X. G. Qiu ◽  
G. X. Chen ◽  
B. R. Zhao ◽  
V. V. Moshchalkov ◽  
Y. Bruynseraede
Keyword(s):  
Vortex Dynamics ◽  
Two Dimensional

scholarly journals The influence of vortices upon the resitance experienced by solids moving through a liquid

1928 ◽  
Vol 119 (781) ◽  
pp. 146-156 ◽  
Keyword(s):  
Perfect Fluid ◽  
Relative Motion ◽  
Constant Velocity ◽  
Fluid Motion ◽  
Resultant Force ◽  
The Other ◽  
Two Dimensional ◽  
Perfect Fluids ◽  
Potential Problems ◽  
The Moment

(1) It is not so long ago that it was generally believed that the "classical" hydrodynamics, as dealing with perfect fluids, was, by reason of the very limitations implied in the term "perfect," incapable of explaining many of the observed facts of fluid motion. The paradox of d'Alembert, that a solid moving through a liquid with constant velocity experienced no resultant force, was in direct contradiction with the observed facts, and, among other things, made the lift on an aeroplane wing as difficult to explain as the drag. The work of Lanchester and Prandtl, however, showed that lift could be explained if there was "circulation" round the aerofoil. Of course, in a truly perfect fluid, this circulation could not be produced—it does need viscosity to originate it—but once produced, the lift follows from the theory appropriate to perfect fluids. It has thus been found possible to explain and calculate lift by means of the classical theory, viscosity only playing a significant part in the close neighbourhood ("grenzchicht") of the solid. It is proposed to show, in the present paper, how the presence of vortices in the fluid may cause a force to act on the solid, with a component in the line of motion, and so, at least partially, explain drag. It has long been realised that a body moving through a fluid sets up a train of eddies. The formation of these needs a supply of energy, ultimately dissipated by viscosity, which qualitatively explains the resistance experienced by the solid. It will be shown that the effect of these eddies is not confined to the moment of their birth, but that, so long as they exist, the resultant of the pressure on the solid does not vanish. This idea is not absolutely new; it appears in a recent paper by W. Müller. Müller uses some results due to M. Lagally, who calculates the resultant force on an immersed solid for a general fluid motion. The result, as far as it concerns vortices, contains their velocities relative to the solid. Despite this, the term — ½ ρq 2 only was used in the pressure equation, although the other term, ρ ∂Φ / ∂t , must exist on account of the motion. (There is, by Lagally's formulæ, no force without relative motion.) The analysis in the present paper was undertaken partly to supply this omission and partly to check the result of some work upon two-dimensional potential problems in general that it is hoped to publish shortly.

scholarly journals Thermal vortex dynamics in a two-dimensional condensate

2000 ◽  
Vol 62 (2) ◽  
pp. 1238-1243 ◽  
Author(s):  
R. Šášik ◽  
Luis M. A. Bettencourt ◽  
Salman Habib
Keyword(s):  
Vortex Dynamics ◽  
Two Dimensional

scholarly journals Vortex dynamics in two-dimensional Josephson junction arrays

2003 ◽  
Vol 68 (5) ◽  
Author(s):  
Md. Ashrafuzzaman ◽  
Massimiliano Capezzali ◽  
Hans Beck
Keyword(s):  
Josephson Junction ◽  
Vortex Dynamics ◽  
Two Dimensional ◽  
Josephson Junction Arrays ◽  
Junction Arrays
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