In this paper we analyse in detail, and for the first time, the rôle of torsion in the dynamics of twisted vortex filaments. We demonstrate that torsion may influence considerably the motion of helical vortex filaments in an incompressible perfect fluid. The binormal component of the induced velocity, asymptotically responsible for the displacement of the vortex filament in the fluid, is closely analysed. The study is performed by applying the prescription of Moore & Saffman (1972) to helices of any pitch and a new asymptotic integral formula is derived. We give a rigorous proof that the Kelvin régime and its limit behaviour are obtained as a limit form of that integral asymptotic formula. The results are compared with new calculations based on the re-elaboration of Hardin's (1982) approach and with results obtained by Levy & Forsdyke (1928) and Widnall (1972) for helices of small pitch, here also re-elaborated for the purpose.

Ricca, R. (1994). The effect of torsion on the motion of a helical vortex filament. JOURNAL OF FLUID MECHANICS, 273, 241-259 [10.1017/S0022112094001928].

The effect of torsion on the motion of a helical vortex filament

RICCA, RENZO
1994

Abstract

In this paper we analyse in detail, and for the first time, the rôle of torsion in the dynamics of twisted vortex filaments. We demonstrate that torsion may influence considerably the motion of helical vortex filaments in an incompressible perfect fluid. The binormal component of the induced velocity, asymptotically responsible for the displacement of the vortex filament in the fluid, is closely analysed. The study is performed by applying the prescription of Moore & Saffman (1972) to helices of any pitch and a new asymptotic integral formula is derived. We give a rigorous proof that the Kelvin régime and its limit behaviour are obtained as a limit form of that integral asymptotic formula. The results are compared with new calculations based on the re-elaboration of Hardin's (1982) approach and with results obtained by Levy & Forsdyke (1928) and Widnall (1972) for helices of small pitch, here also re-elaborated for the purpose.
Articolo in rivista - Articolo scientifico
vortex filament; torsion; Biot-Savart; induction; vortex dynamics
English
1994
273
241
259
open
Ricca, R. (1994). The effect of torsion on the motion of a helical vortex filament. JOURNAL OF FLUID MECHANICS, 273, 241-259 [10.1017/S0022112094001928].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/20229
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