An analytic solution of steady Stokes flow on a rotating spherical cap

Abstract

An analytic solution of two-dimensional steady, linear, viscous flow on a spherical cap - the region of a sphere which lies above (or below) a given plane - rotating about its center is obtained. An inflow and an outflow on the boundary of the spherical section drive the fluid motion. The solution of the stream function is expressed as the Fourier series in longitude and the first-kind associated Legendre functions of complex degrees in cosine of colatitude. The results support the previous study on the approximation analysis and laboratory experiment