Calculation of a Zonal SourceSink Flow in a Rotating Vessel

S. D. Danilov and I. A. Sazonov

Oboukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevskii per. 3, Moscow, 109017 Russia

Received February 19, 1998; in final form November 24, 1998

Abstract—The profile of a zonal source–sink flow in a rotating vessel is calculated using the shallow-water
equations with bottom friction involved. Rectangular and circular geometries and the case of a sloping bottom
are analyzed. The widths of the source–sink zones are estimated and compared to the known results. It is shown
that, if the bulk viscosity is neglected as compared to Ekman friction and the sinks and sources are localized,
the problem under consideration has multiple solutions. The uniqueness of the solution is achieved by taking
into account either an infinitesimal bulk viscosity or an infinitesimal spreading of sources and sinks.

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