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The attraction between a flexible filament and a point vortex

Published online by Cambridge University Press:  09 March 2012

Silas Alben
Silas Alben*
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA
*
†Email address for correspondence: [email protected]
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Abstract

We determine the inviscid dynamics of a point vortex in the vicinity of a flexible filament. For a wide range of filament bending rigidities, the filament is attracted to the point vortex, which generally moves tangentially to it. We find evidence that the point vortex collides with the filament at a critical time, with the separation distance tending to zero like a square root of temporal distance from the critical time. Concurrent with the collision, we find divergences of pressure loading on the filament, filament vortex sheet strength, filament curvature and velocity. We derive the corresponding power laws using the governing equations.

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 697 , 25 April 2012 , pp. 481 - 503
Copyright
Copyright © Cambridge University Press 2012

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Alben supplementary movie

As a supplement to the manuscript ``The attraction between a flexible filament and a point vortex,'' we present a video showing how a point vortex interacts with a passive flexible filament, for various values of filament bending stiffness. We consider a point vortex in a purely inviscid flow. The filament has uniform bending stiffness (with values given in the video frames), is clamped at its left end, and is free at its right end. The first sequence shows the motion of a point vortex around a nearly rigid filament. The green circle is centered at the location of the point vortex and the filament is the black line. The trajectory, shown by the light green line, is nearly periodic. In subsequent clips, we decrease the filament bending stiffness and show the dynamics. In general, the filament is attracted to the vortex, leading to a finite-time collision, with distance tending to zero as the square root of temporal displacement from the collision time. For some values of bending stiffness, we show dynamics for different initial positions. In some clips, we also show a second view at the bottom, which zooms in on the region of the filament near the vortex.

Download Alben supplementary movie(Video)
Video 11.7 MB

Alben supplementary movie

As a supplement to the manuscript ``The attraction between a flexible filament and a point vortex,'' we present a video showing how a point vortex interacts with a passive flexible filament, for various values of filament bending stiffness. We consider a point vortex in a purely inviscid flow. The filament has uniform bending stiffness (with values given in the video frames), is clamped at its left end, and is free at its right end. The first sequence shows the motion of a point vortex around a nearly rigid filament. The green circle is centered at the location of the point vortex and the filament is the black line. The trajectory, shown by the light green line, is nearly periodic. In subsequent clips, we decrease the filament bending stiffness and show the dynamics. In general, the filament is attracted to the vortex, leading to a finite-time collision, with distance tending to zero as the square root of temporal displacement from the collision time. For some values of bending stiffness, we show dynamics for different initial positions. In some clips, we also show a second view at the bottom, which zooms in on the region of the filament near the vortex.

Download Alben supplementary movie(Video)
Video 30.8 MB