Starting jets and vortex ring pinch-off

Starting jet is commonly defined as the transient motion produced when a viscous incompressible fluid is forced from an initial state of rest Cantwell (Journal of Fluid Mechanics, 173, 159-189 [6]). The applied force can be time dependent in the form of an impulsive, step or ramp function acting at a point or along a line. Starting jet can be used in fundamental study of vortex ring dynamics, synthetic jets, mixing enhancement, and vortex-enhanced unsteady propulsion systems. Researches related to starting jets have been carried out broadly in two directions. The first direction is focused on the underlying mechanism for the vortex ring pinch-off, which is defined as the process whereby a forming vortex ring is no longer able to absorb vorticity flux from the jet source via the separated shear layer. Several theoretical models are proposed to predict a critical time scale for the pinchoff process, dubbed as the formation number F, for different flow conditions. The second direction is focused on its practical applications in entrainment enhancement as well as pulsed-jet propulsion systems. Specifically, due to the restricted vortex ring formation in starting jet, the propulsive efficiency can be effectively improved over the steady jet propulsion by increasing the generated thrust via the vortex overpressure in the near-wake and by decreasing the kinetic energy loss in the wake via vortex entrainment. In this chapter, we intend to provide the readers with some basic ideas on the dynamic process of vortex ring formation in a starting jet, and its practical application in nature and engineering fields. This chapter is divided into four parts. The first part provides a brief introduction of the starting jet and the phenomenon of vortex ring pinch-off. The discussion of the underlying mechanisms and its theoretical explanation are provided in part two. In the third part, the practical application of starting jets in engineering systems will be explained and discussed. This chapter ends with a summary and an outlook for future study on the starting jet.