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

• Published in: Fluid Dynamics Research
• Main Authors: Kitauchi, Hideaki, Ikeda, Motoyoshi
• Format: Article in Journal/Newspaper
• Language: English
• Published: IOP Publishing
• Subjects: Analytic solution; Stationary; Stokes flow; Rotation; Polar cap; 423; North Pole
• Online Access: http://hdl.handle.net/2115/39627; https://doi.org/10.1088/0169-5983/41/4/045505

An analytic solution of two-dimensional, steady, linear, viscous flow on a polar cap-polar region of a sphere that lies above (or below) a given plane normal to the rotation axis-rotating about its center is obtained. Inflow and outflow on the boundary of the polar cap drive the fluid motion. The solution of the stream function is expressed as the Fourier series in longitudes and the associated Legendre functions of complex degrees in cosines of colatitudes. The fluid particles move almost along lines of constant latitude, some circulate cyclonically and the others anticyclonically, in the geostrophic balance everywhere except near the north pole where the flow is relatively slow and the viscous force dominates over the Coriolis force. Our results support the approximation analysis and laboratory experiment studied by Imawaki and Takano (Deep-Sea Res. 21, 69-77, 1974).