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Volume 1,     Number 4,     Fall 1993

 

ANALYSIS OF THE MODIFIED OSEEN EQUATIONS
USING ORTHOGONAL FUNCTION EXPANSIONS
S. KOCABIYIK

Abstract. The two-dimensional Navier-Stokes equations, describing a steady flow of a viscous incompressible fluid past a circular cylinder, are analyzed by using an orthogonal function expansion in an angular variable on the basis of the modified Oseen approximation due to Southwell and Squire. The analysis is developed in terms of the scalar vorticity and stream function. An asymptotic solution to the vorticity is obtained separately from the stream function using modified Mathieu functions, the determination of which can be effected by successive approximations in terms of the low Reynolds number. The usefulness of the modified Oseen type of successive approximation in dealing with the Navier-Stokes equations is confirmed by estimating the critical value of the Reynolds number, and some suggestions for extension to the full Navier- Stokes equations are made.

 

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