Sources and sinks on a β-earth

This paper is concerned with flow on a β-earth toward a sink. A perfect-fluid solution for a strong sink at the equator midway between two rigid latitude circles shows that the streamline that divides flow from the west and flow from the east is a straight, north-south line through the sink when the β-effect is neglected, but tilts toward the west when it is taken into account. The β-effect also causes the sink to draw more strongly from its own latitude in the region west of the sink and less strongly from its own latitude east of the sink. This agrees with qualitative reasoning based on the vorticity equations. Solutions are also found for a weak, viscous sink at an arbitrary latitude. Approximate analytical expressions, valid far from the origin, indicate greatly different flow patterns in the western and eastern sectors. In the former the motion is divided into two components. One is a jet at the latitude of the sink, and this jet carries the entire flux into the sink. The other corresponds to motion induced by the basic rotation itself and is a flattened portion of a vortex in the same region occupied by the westerly jet. The jet component dominates at sufficiently great distances. The flow from the east dies off exponentially with distance and has a wave-like character.