The formation process of annular starting jets

The formation and evolution process of the outer vortex ring (denoted as OV0) in annular starting jets has been studied numerically at stroke ratio, and Reynolds number, where is the outer diameter of orifice, is the length of the fluid column, and are the ratio and difference between inner and outer radii of the annular orifice, respectively. The initial formation process of OV0 is found to be similar to that of the leading vortex ring in a circular starting jet, but the circulation strength is relatively lower and decreases gradually with increasing. The pinch-off process will also appear after OV0 grows to a certain size but is different from that of the circular starting jet. On one hand, OV0 is stretched and deformed by the strain field generated by the trailing jet's instability, and vorticity would be shed. On the other hand, OV0 accelerates the irrotational fluids around it under viscous action so as to form the induced velocity field, which would consume energy causing it to shed vorticity further under the limit of the Kelvin-Benjamin variational principle. Furthermore, OV0 would eventually become a stable vortex ring whose non-dimensional circulation ) is found to be between 0.59-0.62 and it would not change with different at, which is much less than the 2-2.5 of circular starting jets.