Abstract
A spiral point vortex, which is a point vortex with a source-sink structure, appears when we consider a two-dimensional cross section of a straight vortex line with a uniform flow in its axial direction in three-dimensional space. In the present paper, we present a computational theory for the motion of spiral point vortices in two-dimensional exterior domains that contain multiple rectilinear line segments as boundaries, called slit domains. The theory consists of the evolution equation for spiral point vortices in multiply connected domains and a numerical procedure to construct conformal mappings from multiply connected domains with circular boundaries onto given slit domains. It is applicable to many flow problems arising in biofluids and environmental flows. As an example, we apply the theory to the flow problem of finding force-enhancing equilibria consisting of two spiral point vortices in a slit domain with two parallel plates in the presence of a uniform flow, which is a two-dimensional model of a wind-turbine with vertical blades.
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Aoyama, N., Sakajo, T. & Tanaka, H. A computational theory for spiral point vortices in multiply connected domains with slit boundaries. Japan J. Indust. Appl. Math. 30, 485–509 (2013). https://doi.org/10.1007/s13160-013-0113-5
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DOI: https://doi.org/10.1007/s13160-013-0113-5