Point vortex dynamics within a background vorticity patch

2001 ◽  
Vol 13 (3) ◽  
pp. 677-691 ◽  
Author(s):  
Dezhe Z. Jin ◽  
Daniel H. E. Dubin
Keyword(s):  
Vortex Dynamics ◽  
Point Vortex

Point vortex dynamics in a magnetized plasma

1994 ◽  
Author(s):  
Mitsuo Kono ◽  
Hideaki Shibahara ◽  
Kentaro Yabuki
Keyword(s):  
Vortex Dynamics ◽  
Point Vortex ◽  
Magnetized Plasma

scholarly journals Network-theoretic approach to sparsified discrete vortex dynamics

2015 ◽  
Vol 768 ◽  
pp. 549-571 ◽  
Author(s):  
Aditya G. Nair ◽  
Kunihiko Taira
Keyword(s):  
Vortex Dynamics ◽  
Point Vortex ◽  
Spectral Graph Theory ◽  
Theoretic Approach ◽  
Dynamics Model ◽  
Discrete Vortex ◽  
Sparse Graphs ◽  
Graph Representations ◽  
Vortex Interactions ◽  
Two Dimensional Flow

We examine discrete vortex dynamics in two-dimensional flow through a network-theoretic approach. The interaction of the vortices is represented with a graph, which allows the use of network-theoretic approaches to identify key vortex-to-vortex interactions. We employ sparsification techniques on these graph representations based on spectral theory to construct sparsified models and evaluate the dynamics of vortices in the sparsified set-up. Identification of vortex structures based on graph sparsification and sparse vortex dynamics is illustrated through an example of point-vortex clusters interacting amongst themselves. We also evaluate the performance of sparsification with increasing number of point vortices. The sparsified-dynamics model developed with spectral graph theory requires a reduced number of vortex-to-vortex interactions but agrees well with the full nonlinear dynamics. Furthermore, the sparsified model derived from the sparse graphs conserves the invariants of discrete vortex dynamics. We highlight the similarities and differences between the present sparsified-dynamics model and reduced-order models.

scholarly journals Winding of a Brownian particle around a point vortex

2019 ◽  
Vol 377 (2158) ◽  
pp. 20180347
Author(s):  
Huanyu Wen ◽  
Jean-Luc Thiffeault
Keyword(s):  
Numerical Simulations ◽  
Gamma Distribution ◽  
Theta Function ◽  
Vortex Dynamics ◽  
Brownian Particle ◽  
Point Vortex ◽  
Theme Issue ◽  
Drift Term ◽  
Inverse Gamma ◽  
Winding Angle

We derive the asymptotic winding law for a Brownian particle in the plane subjected to a tangential drift due to a point vortex. For winding around a point, the normalized winding angle converges to an inverse Gamma distribution. For winding around a disc, the angle converges to a distribution given by an elliptic theta function. For winding in an annulus, the winding angle is asymptotically Gaussian with a linear drift term. We validate our results with numerical simulations. This article is part of the theme issue ‘Topological and geometrical aspects of mass and vortex dynamics’.

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.

A dissipative point-vortex model for nearshore circulation

2007 ◽  
Vol 589 ◽  
pp. 455-478 ◽  
Author(s):  
E. TERRILE ◽  
M. BROCCHINI
Keyword(s):  
Vortex Dynamics ◽  
Large Scale ◽  
Current System ◽  
Single Point ◽  
Point Vortex ◽  
Breaking Wave ◽  
Rip Current ◽  
Practical Applications ◽  
Vortex Model ◽  
Point Vortex Model

The hydrodynamic circulation of a nearshore region with complex bathymetry is inves- tigated by means of a point-vortex approach similar, but more complete and suited to practical applications, to that of Kennedy (J. Fluid Mech. vol. 497, 2003, p. 225). The generation and dissipation of each single-point vortex are analysed in detail to obtain a complete description of the vortex dynamics. In particular, we clarify how the mechanism for the generation of breaking-wave-induced macrovortices (large-scale two-dimensional horizontal vortices) can be practically implemented and we discuss in detail the mechanism leading to the dissipation of the circulation assigned to each vortex. Available approximate relations for the rate of generation of bar vortices are placed in context and discussed in detail, and novel approximate relations for the shore vortex generation and for the vortex viscous dissipation are proposed, the latter largely improving the description of the point vortex dynamics. Results have been obtained using three ‘typical’ rip-current bathymetries for which we also test qualitatively and quantitatively the model comparing the vorticity dynamics with the results obtained by means of both wave-resolved and wave-averaged circulation models. A comparison of dynamically equivalent flow configurations shows that the dissipative point-vortex model solutions, neglecting any influence of the wave field, provide rip current velocities in good agreement with both types of numerical solution. A more complete description of the rip current system, not limited to the rip-neck region as given by Kennedy (2003) by mean of an inviscid model, has been achieved by including dissipative effects.

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