Shear reduction of 2D point vortex diffusion

2002 ◽  
Author(s):  
Daniel H. E. Dubin
Keyword(s):  
Point Vortex ◽  
Vortex Diffusion

Chaos in body–vortex interactions

2010 ◽  
Vol 466 (2119) ◽  
pp. 1871-1891 ◽  
Author(s):  
Johan Roenby ◽  
Hassan Aref
Keyword(s):  
Body Shape ◽  
Mass Density ◽  
Relative Equilibrium ◽  
Large Body ◽  
Point Vortex ◽  
Cylindrical Body ◽  
The Body ◽  
Body Motion ◽  
Single Vortex ◽  
Vortex Interactions

The model of body–vortex interactions, where the fluid flow is planar, ideal and unbounded, and the vortex is a point vortex, is studied. The body may have a constant circulation around it. The governing equations for the general case of a freely moving body of arbitrary shape and mass density and an arbitrary number of point vortices are presented. The case of a body and a single vortex is then investigated numerically in detail. In this paper, the body is a homogeneous, elliptical cylinder. For large body–vortex separations, the system behaves much like a vortex pair regardless of body shape. The case of a circle is integrable. As the body is made slightly elliptic, a chaotic region grows from an unstable relative equilibrium of the circle-vortex case. The case of a cylindrical body of any shape moving in fluid otherwise at rest is also integrable. A second transition to chaos arises from the limit between rocking and tumbling motion of the body known in this case. In both instances, the chaos may be detected both in the body motion and in the vortex motion. The effect of increasing body mass at a fixed body shape is to damp the chaos.

On point vortex models of exotic bluff body wakes

2014 ◽  
Vol 46 (6) ◽  
pp. 061410 ◽  
Author(s):  
Mark A Stremler ◽  
Saikat Basu
Keyword(s):  
Bluff Body ◽  
Point Vortex

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

scholarly journals Collapse of n Point Vortices, Formation of the Vortex Sheets and Transport of Passive Markers

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 943
Author(s):  
Henryk Kudela
Keyword(s):  
Differential Equations ◽  
Point Vortex ◽  
Optimization Procedure ◽  
Vortex Sheet ◽  
Point Vortices ◽  
Vortex Sheets ◽  
Impermeable Barrier ◽  
Initial Location ◽  
Passive Tracers ◽  
Initial Iterate

In this paper, the motion of the n-vortex system as it collapses to a point in finite time is studied. The motion of vortices is described by the set of ordinary differential equations that we are able to solve analytically. The explicit formula for the solution demands the initial location of collapsing vortices. To find the collapsing locations of vortices, the algebraic, nonlinear system of equations was built. The solution of that algebraic system was obtained using Newton’s procedure. A good initial iterate needs to be provided to succeed in the application of Newton’s procedure. An unconstrained Leverber–Marquart optimization procedure was used to find such a good initial iterate. The numerical studies were conducted, and numerical evidence was presented that if in a collapsing system n=50 point vortices include a few vortices with much greater intensities than the others in the set, the vortices with weaker intensities organize themselves onto the vortex sheet. The collapsing locations depend on the value of the Hamiltonian. By changing the Hamiltonian values in a specific interval, the collapsing curves can be obtained. All points on the collapse curves with the same Hamiltonian value represent one collapsing system of vortices. To show the properties of vortex sheets created by vortices, the passive tracers were used. Advection of tracers by the velocity induced by vortices was calculated by solving the proper differential equations. The vortex sheets are an impermeable barrier to inward and outward fluxes of tracers. Arising vortex structures are able to transport the passive tracers. In this paper, several examples showing the diversity of collapsing structures with the vortex sheet are presented. The collapsing phenomenon of many vortices, their ability to self organize and the transportation of the passive tracers are novelties in the context of point vortex dynamics.

Point Source and Point Vortex in the Hodograph Plane

1957 ◽  
Vol 24 (2) ◽  
pp. 183-190
Author(s):  
H. Poritsky ◽  
R. A. Powell
Keyword(s):  
Point Source ◽  
Point Vortex ◽  
Series Expansions ◽  
Hodograph Plane

Abstract Hodograph plane solutions possessing point-source and point-vortex singularities are obtained by means of series expansions in product solutions.

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