A criterion for vortex breakdown

Abstract

A criterion for the onset of vortex breakdown over a wide range of the Reynolds number is proposed. Based upon previous experimental, theoretical, and numerical studies, as well as a new numerical study, an appropriately defined local Rossby number is used to delineate the region where breakdown occurs. Comparisons are made with previously suggested criticality parameters and the unique features of the proposed Rossby number parameter are shown. A number of previous theoretical studies concentrating on inviscid standing-wave analyses for trailing wing-tip vortices are reviewed and reinterpreted, along with the previous numerical and experimental studies, in terms of the Rossby number parameter. For the case of trailing wing-tip-type vortices, it is shown that previous numerical studies were performed at lower Reynolds numbers than the corresponding laboratory experiments. Utilizing a consistently defined Reynolds number, Rossby number–Reynolds number plots of these previous vortex breakdown studies, for both trailing wing-tip and leading-edge vortices, are obtained. A criticality condition is identified for both types of vortices.