Theoretical and experimental investigation of the structure of azimuthal source–sink flow in a rotating shallow water layer

Abstract

The structure of source-sink flow in a rotating shallow water layer is studied both theoretically and experimentally. Theoretical calculations are carried out in the framework of the nonlinear model of Ekman boundary layer based on the description of advective terms in the geostrophic momentum approximation. The radial profiles of azimuthal velocity are derived analytically in the small Rossby number limit. It has been shown that the structure of these profiles varies essentially when changing the direction of a radial flow. The velocity profile is strictly monotonic for cyclonic flow (radial flow is directed to the centre) and non-monotonic with maximum near the source-for anticyclonic flow. These results are in agreement with theoretical results by Danilov, Sazonov, derived in the framework of vertically integrated model. The experimental part of the work is carried out on the special experimental apparatus at Abastumani Astrophysical Observatory. The measured radial profiles of the fluid depth and azimuthal velocity produced by concentric sources and sinks located at the bottom of the rotating parabolic vessel are presented. The dependence of these profiles on the intensity of the source-sink system is investigated. It is shown that theoretical results reproduce the main features of the profiles measured in experiments.