A new approach to the classical Stokes flow problem: Part I Methodology and first-order analytical results

The problem of determining the axisymmetric Stokes flow past an arbitrary body, the boundary shape of which can be represented by an analytic function, is examined by developing an exact method. An appropriate nonorthogonal coordinate system is introduced, and it is shown that the Hilbert space to which the stream function belongs is spanned by the set of Gegenbauer polynomials based on the physical argument that the drag on a body should be finite. The partial differential equation of the original problem is then reduced to two simultaneous vector differential equations. By the truncation of this infinite-dimensional system to the one-dimensional subspace, an explicit analytic solution to the Stokes equation valid for all bodies in question is obtained as a first approximation.