Formation of Leading Vortex Pair in Two-Dimensional Starting Jets

The vortex formation process in a two-dimensional starting jet at Reynolds numbers ranging from 1500 to 3400 has been investigated experimentally. The present results show that the formation of leading vortex pair can be restricted by the growth of secondary vortices from trailing shear-layer instability. The detachment of the leading vortex pair is found to be analogous to the pinchoff process of an axisymmetric vortex ring formation. The critical formation number F for the vortex pair is identified to be around 7, higher than the value of 4 for the vortex ring formation. Because of the nonsaturated state of the vortex pair, the main mechanisms responsible for the vortex ring pinchoff (i.e., the Kelvin-Benjamin variational principle) may not be applicable in the two-dimensional cases. As such, the vortex pair pinchoff at higher Reynolds number can be attributed largely to the roll-up and growth of the secondary vortices in the trailing shear layer. The present results suggest that the shear-layer instability appears to be a major physical mechanism for the phenomenon of limited vortex formation in more general vortex-shedding flows, complementary to the existing theory based on the Kelvin-Benjamin variational principle.