## Chaos in body-vortex interactions

Publication: Research - peer-review › Journal article – Annual report year: 2010

### Standard

**Chaos in body-vortex interactions.** / Pedersen, Johan Rønby; Aref, Hassan.

Publication: Research - peer-review › Journal article – Annual report year: 2010

### Harvard

*Royal Society of London. Proceedings. Mathematical, Physical and Engineering Sciences*, vol 466, no. 2119, pp. 1871-1891. DOI: 10.1098/rspa.2009.0619

### APA

*Royal Society of London. Proceedings. Mathematical, Physical and Engineering Sciences*,

*466*(2119), 1871-1891. DOI: 10.1098/rspa.2009.0619

### CBE

### MLA

*Royal Society of London. Proceedings. Mathematical, Physical and Engineering Sciences*. 2010, 466(2119). 1871-1891. Available: 10.1098/rspa.2009.0619

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### Author

### Bibtex

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### RIS

TY - JOUR

T1 - Chaos in body-vortex interactions

AU - Pedersen,Johan Rønby

AU - Aref,Hassan

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - body-vortex interaction

U2 - 10.1098/rspa.2009.0619

DO - 10.1098/rspa.2009.0619

M3 - Journal article

VL - 466

SP - 1871

EP - 1891

JO - Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences

T2 - Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences

JF - Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences

SN - 1364-5021

IS - 2119

ER -