The breakdown of jet flows in a low-Rossby-number rotating fluid

Abstract

The behaviour of steady jet-like flows is examined in a low-Rossby-number rotating fluid. Unlike the corresponding non-rotating flow, the momentum flux of a jet in a rotating fluid is not conserved with distance downstream and, as a consequence, the jet loses all of its momentum at a finite distance from the source, apparently developing a singularity as this occurs. The asymptotic properties of the flow leading up to this singular point are calculated for jets of various inflow widths and a structure which resolves the singularity that occurs in each of these cases is described. The properties on the approach to the singularity are shown to be similar to those of the exact solution described by Gadgil [12]. Both the asymptotic structure and the resolution of the singularity are, however, applicable to the expected breakdown of any form of jet in rotating fluid under similar conditions. The consequences of this are discussed, particularly in relation to the separated-flow structure proposed for motion past a cylindrical obstacle in Page [3].

Flow past a circular cylinder on a β-plane

“…where the constant of integration is evaluated by noting that since u is of order unity outside the layer, iivanishes to leading order as p-t 00. This is the equation for 'bottom frictional' jets discussed by Gadgil (1971) and for 'wide' jets by Page & Eabry (1990).…”