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On the curvature and torsion of an isolated vortex filament

Published online by Cambridge University Press:  28 March 2006

Robert Betchov
Robert Betchov
Affiliation:
Aerospace Corporation, E1 Segundo, California
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Abstract

We consider a very thin vortex filament in an unbounded, incompressible and inviscid fluid. The filament is not necessarily plane. Each portion of the filament moves with a velocity that can be approximated in terms of the local curvature of the filament. This approximation leads to a pair of intrinsic equations giving the curvature and the torsion of the filament, as functions of the time and the arc length along the filament. It is found that helicoidal vortex filaments are elementary solutions, and that they are unstable.

The intrisic equations also suggest a linear mechanism that tends to produce concentrated torsion and a non-linear mechanism tending to disperse such singularities.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 22 , Issue 3 , July 1965 , pp. 471 - 479
Copyright
© 1965 Cambridge University Press

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References

Hama, F. R., 1962 Progressive deformation of a curved vortex filament by its own induction. Phys. Fluids, 5, 1156–62.Google Scholar
Hama, F. R., 1963 Progressive deformation of a perturbed line vortex filament. Phys. Fluids, 6, 526–34.Google Scholar
Kelvin, Lord 1880 Mathematical and Physical Papers, vol. 4, p. 152. Cambridge University Press.
Prandtl, L. & Tietjens, O. G. 1934 Fundamentals of Hydro- and Aero-Mechanics, 1st Ed., 90. New York: McGraw-Hill.