Hideaki Kitauchi and Motoyoshi Ikeda 2009 Fluid Dyn. Res. 41 045505 doi:10.1088/0169-5983/41/4/045505
Hideaki Kitauchi1 and Motoyoshi Ikeda2
Show affiliationsCommunicated by Y Hayashi
An analytic solution of two-dimensional, steady, linear, viscous flow on a polar cap—the 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. Fluid particles move almost along lines of constant latitude, some circulate cyclonically and 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 (1974 Deep-Sea Res. 21 69–77).
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
15A18 Eigenvalues, singular values, and eigenvectors
86A05 Hydrology, hydrography, oceanography (See also 76Bxx, 76E20, 76Q05, 76Rxx, 76U05)
Issue 4 (August 2009)
Received 26 April 2007, in final form 9 July 2008
Published 12 May 2009
Hideaki Kitauchi and Motoyoshi Ikeda 2009 Fluid Dyn. Res. 41 045505
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