Date of Award


Degree Type


Degree Name

Doctor of Philosophy


The primary objective of this work is to analyze the steady two-dimensional flow of a viscous incompressible fluid past a conformally-mappable cylinder in an unbounded field. The main concern is the correct satisfaction of the boundary conditions at large distances from the cylinder. It is shown that the steady-state asymmetrical flow problem needs careful examination, particularly with regard to the satisfaction of these conditions. A general method is developed to solve this class of problem, under the assumption that flow is governed by the Oseen linearized equations of motion. The method is based on satisfaction of the proper conditioning for the vorticity of integral type. This is considered as a very important part of the solution procedure since the integral conditions ensure both the correct decay of the vorticity at large distances from the cylinder and satisfaction of the physically essential results for the existence of the flow. For Oseen flow the method enables one to obtain the vorticity separately from the stream function.;As an example of the application of the method, the uniform flow past an elliptic cylinder at an arbitrary angle of incidence at low Reynolds number R sc E is considered. An analytical expression for the vorticity on the surface of the elliptic cylinder is obtained correct to the order of (R sc E) (lnR sc E) {dollar}\sp{lcub}-1{rcub}{dollar}, the lowest order term being O((lnR sc E) {dollar}\sp{lcub}-1{rcub}).{dollar} The leading terms for the asymptotic expansions for the life, drag coefficients and the circulation round a large contour surrounding the elliptic cylinder are determined in terms of R sc E. In this case the Reynolds number R sc E is based on the length of the major axis of the ellipse. The method is also applied to the cases of symmetrical and asymmetrical flows past circular cylinders. A paradox is obtained for asymmetrical flow generated by a rotating circular cylinder. The first Oseen paradox may be stated as " No steady two-dimensional asymmetrical Oseen flow of a viscous incompressible fluid past a rotating circular cylinder is possible ". It is found to be impossible to obtain a solution in this case in which the circulation is non-zero.



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