Journal of Fluid Mechanics

Low-Reynolds-number flow past an elliptic cylinder

Kazuhito  Shintani a1, Akira  Umemura a2 and Akira  Takano a3
a1 Department of Mechanical Engineering, University of Electro-Communications, Chofu, Tokyo, Japan
a2 Department of Mechanical Engineering, Yamagata University, Yonezawa, Yamagata, Japan
a3 Department of Aeronautics, University of Tokyo, Bunkyo-ku, Tokyo, Japan

Article author query
shintani k   [Google Scholar] 
umemura a   [Google Scholar] 
takano a   [Google Scholar] 


The primary objective of this paper is to obtain the detailed description of the flow field near an elliptic cylinder that is placed perpendicularly in a uniform stream at low Reynolds number. Attention is paid to the shape effects due to the flattening of the cylinder and to the inertial effects of the fluid. The analysis resorts to the method of matched asymptotic expansions. The main part of the inner expansion describes the near flow field as a Stokes flow, which is characterized by the singularities arranged at the two foci of the ellipse. The first three terms $O({\mathbb R}) ({\mathbb R}$ = Reynolds number) in the inner expansion are developed, and the flow aspects under the influence of the fluid inertia are investigated. The streamline patterns with one or two vortices round a finite flat plate of zero thickness, which is a special case of the elliptic cylinder, are presented.

(Published Online April 20 2006)
(Received May 27 1982)
(Revised July 26 1983)