The Initial Flow Past AN Impulsively Started Elliptic Cylinder by the Method of Matched Asymptotic Expansions.

The initial flow of a viscous, incompressible fluid past an impulsively started elliptic cylinder at several angles of attack is studied by the method of matched asymptotic expansions. The formulation consists simply of the vorticity transport equation, subject to the appropriate initial and boundary conditions. The assumptions are finite but large Reynolds numbers and small times. Analytical solutions for the inner and outer flow fields are obtained to the third order, for which the pressure varies across the boundary layer. A uniformly valid composite solution in terms of exponential and error functions is then constructed from the inner and outer solutions. The REDUCE symbolic manipulation language is used to facilitate the analysis. Results are presented for the flow past a 2:1 elliptic cylinder in terms of: patterns of streamlines; tangential velocity profiles; separation times; surface vorticity distributions and pressure, drag and lift coefficients. The streamline patterns resemble the experimental results of Honji. The separation times are shown to increase with decreasing Reynolds numbers following the trend obtained numerically for the circular cylinder by Collins and Dennis. Application of Pade' approximants indicates that the solution improves with decreasing angle of attack. (Copies available exclusively from Micrographics Department, Doheny Library, USC, Los Angeles, CA 90089.).