Abstract
The velocity field induced by semi-infinite and infinite helical filaments is studied in this chapter. The exact expressions from Hardin are provided in terms of modified Bessel functions. The approximate expressions from Lerbs and Wrench are given. The link between Okulov’s relation and Wrench’s relation is shown. The formulae are given for several helical filaments equally distributed along the azimuth. A Matlab source code to calculate the induced velocities is given in Sect. 14.3.2. The helical filament solutions are used in this book in Chap. 14 to compute Goldstein’s circulation or in Chap. 20 to derive a new analytical tip-loss factor.
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