Motion and flow topology of multiple helical vortices

Abstract eng:
A set of equal, coaxial, symmetrically-arranged helical vortices translate and rotate steadily while the vortices preserve their shape and relative position in an unbounded, ideal fluid (Joukowsky 1912). We obtained the corresponding linear and angular velocities (U and Ω, respectively) as the sum of the mutually induced velocities found by Okulov (2004) and the self-induced velocities found by Velasco Fuentes (2016). Numerical computation of the velocities with the Biot-Savart law, and numerical simulation of the vortex motion with a 3D vortex-in-cell method verified that our theoretical results are accurate for any number of vortices and over the whole range of values of the vortices’ pitch and radius. An analysis of the flow topology in a reference system that translates with velocity U and rotates with angular velocity Ω served to determine the capacity of the vortices to carry fluid.

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