Analytical solution for self-induced motion of a helical vortex with a Gaussian core

V. L. Okulov*, Y. Fukumoto

*Corresponding author for this work

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The paper presents an analytical solution for helical vortices with a Gaussian vorticity distribution in the core, which is confirmed by experimental and numerical simulations. This result is obtained by extending the Dyson method to the Biot–Savart law. Previously, analytical solutions were found and studied only for vortices with constant vorticity distribution in the core (a Rankine-type vortex core). One of the important issues raised during the discussion is the difference between self-induced movements of helical structures with both types of vortex core. The proposed solutions are important for the fundamental understanding and description of the behavior of helical eddy flows in various fields of industry and in nature. Examples include tip vortices behind the rotors of wind or hydro turbines, tornadoes, or axial vortices in aerodynamic devices such as vortex apparatuses and generators; cyclone separators, combustion chambers, etc.
Original languageEnglish
JournalThermophysics and Aeromechanics
Issue number4
Pages (from-to)481-488
Publication statusPublished - 2020


  • Vortex dynamics
  • Helical vortex
  • Gaussian vorticity distribution
  • Self-induced rotation


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