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

H. Kitauchi, H. Simmons, M. Ikeda
Oceans '04 MTS/IEEE Techno-Ocean '04 (IEEE Cat. No.04CH37600)  
An analytic solution of steady linear viscous flow on a spherical cap ( Figure 1 ) rotating about its center is obtained. An inflow and an outflow on the boundary of spherical section drive the fluid motion. The solution of the stream function ψ(ϑ, ϕ) is expressed as the Fourier series in longitude ϕ ∈ [0, 2π) and the first-kind associated Legendre functions of complex degrees in colatitude ϑ ∈ [0, ϑ b ].
doi:10.1109/oceans.2004.1406346 fatcat:ekq2jhmiy5hgbgsjwlhb6ualem