# On motion of a double helical vortex in a cylindrical tube

## Abstract

New approach is developed for the velocity estimation of a double helical vortex motion in boundless space as well as in a cylindrical tube.

The system under consideration is two thin helical vortices winding around common axis and propagating in surrounding irrotational fluid. The problem on the determination of the velocity of the vortices motion is solved with help of formulae describing the velocity field induced by infinitely thin helical vortex inside a cylindrical tube (Okulov 1995) and using the technique of the singularities separation from this solution (Kuibin & Okulov 1998). As a result an analytical formula for the vortices propagation velocity is found with account for the self and mutual induced velocities, influence of the solid boundary and translational motion. The formula contains infinite series from the modified Bessel functions. Nonetheless it is shown that impact of these series is small enough and can be neglected to give a more simple formula.

## Keywords

Cylindrical Tube Modify Bessel Function Vortex Filament Vortex Chamber Helix Pitch## Preview

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