Review Article

The Contribution of Kawada to the Analytical Solution for the Velocity Induced by a Helical Vortex Filament

[+] Author and Article Information
Yasuhide Fukumoto

Institute of Mathematics for Industry,
Kyushu University,
744 Motooka, Nishi-ku,
Fukuoka 819-0395, Japan
e-mail: yasuhide@imi.kyushu-u.ac.jp

Valery L. Okulov

Wind Energy Department,
Technical University of Denmark,
Nils Koppels Alle,
Building 403,
Lyngby DK-2800, Denmark;
Institute of Thermophysics,
Siberian Branch of the Russian
Academy of Sciences,
Lavrentyev Avenue, 1,
Novosibirsk 630090, Russia
e-mail: vaok@dtu.dk

David H. Wood

Schulich School of Engineering,
University of Calgary,
2500 University Drive NW,
Calgary T2N 1N4, Canada
e-mail: dhwood@ucalgary.ca

1Corresponding author.

Manuscript received April 28, 2015; final manuscript received November 3, 2015; published online December 1, 2015. Assoc. Editor: Herman J. H. Clercx.

Appl. Mech. Rev 67(6), 060801 (Dec 01, 2015) (6 pages) Paper No: AMR-15-1048; doi: 10.1115/1.4031964 History: Received April 28, 2015; Revised November 03, 2015

The basic solution for the velocity induced by helical vortex filament is well known as Hardin's solution, published in 1982. A study of early publications on helical vortices now shows that the Japanese scientist Kawada from Tokyo Imperial University also produced many of these results in 1936, which predates Hardin by 46 years. Consequently, in order to honor both, we have studied their derivations to establish the originality of both solutions.

Copyright © 2015 by ASME
Topics: Vortices
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Grahic Jump Location
Fig. 1

Sandi Kawada (Reproduced from [38] with permission of the journal. Copyright 1970 by Journal of the Japan Society of Aeronautical Engineering)

Grahic Jump Location
Fig. 2

The geometry of helical vortex filament

Grahic Jump Location
Fig. 3

A structure of vorticity: (a) the Goldstein's vortex sheet and (b) the associated vortex system for Kawada's consideration with a constant circulation along radial direction of vortex sheet




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