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Title: Power-series solution for the two-dimensional inviscid flow with a vortex and multiple cylinders
Authors: Pashaev, Oktay
Yılmaz, Oğuz
Keywords: Circle theorem
Hydrodynamic interaction
Point vortex
Power-series solution
Vortex dynamics
Issue Date: 2009
Publisher: Springer Verlag
Source: Pashaev, K. and Yılmaz, O. (2009). Power-series solution for the two-dimensional inviscid flow with a vortex and multiple cylinders. Journal of Engineering Mathematics, 65(2), 157-169. doi:10.1007/s10665-009-9271-5
Abstract: The problem of a point vortex and N fixed cylinders in a two-dimensional inviscid fluid is studied and an analytical-numerical solution in the form of an infinite power series for the velocity field is obtained using complex analysis. The velocity distribution for the case of two cylinders is compared with the existing results of the problem of a vortex in an annular region which is conformally mapped onto the exterior of two cylinders. Limiting cases of N cylinders and the vortex, being far away from each other are studied. In these cases, "the dipole approximation" or "the point-island approximation" is derived, and its region of validity is established by numerical tests. The velocity distribution for a geometry of four cylinders placed at the vertices of a square and a vortex is presented. The problem of vortex motion with N cylinders addressed in the paper attracted attention recently owing to its importance in many applications. However, existing solutions using Abelian function theory are sophisticated and the theory is not one of the standard techniques used by applied mathematicians and engineers. Moreover, in the N ≥ 3 cylinder problem, the infinite product involved in the presentation of the Schottky-Klein prime function must also be truncated. So, the approach used in the paper is simple and an alternative to existing methods. This is the main motivation for this study.
ISSN: 0022-0833
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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