Formation of vortex dipoles

Abstract

Evolution of a two-dimensional flow induced by a jet ejected from a nozzle of finite size is studied experimentally. Vortex dipole forms at the front of the developing flow while a trailing jet establishes behind the dipole. The dynamics of the flow is discussed on the basis of detailed measurements of vorticity and velocity fields which are obtained using particle image velocimetry. It is found that dipoles do not separate ͑pinch-off͒ from the trailing jet for values of the stroke ratio up to 15, which fact can be contrasted with the behavior of vortex rings reported previously by other authors. A characteristic time scale that is defined differently from the formation time of vortex rings can be introduced. This time scale ͑startup time͒ indicates the moment when the dipole starts translating after an initial period when it mainly grows absorbing the jet from the nozzle. A simple model that considers the competing effects of expansion and translation is developed to obtain an estimate of the dimensionless startup time. The dynamics of a dipole after the formation is characterized by a reduced flux of vorticity from the jet. The dipole moves forward with constant speed such that a value of the ratio of the speed of propagation of the dipole to the mean velocity of the jet is found to be 0.5. A universality of this ratio is explained in the framework of a model based on conservation of mass and momentum for the moving dipole.

Pinch-off of non-axisymmetric vortex rings

“…The absence of the crescent vortex might be indicative of a change in the vortex formation process for very-high-aspectratio orifices. Such a change is consistent with the two-dimensional rollup observed in the limiting case of extremely thin slits (Afanasyev 2006;Pedrizzetti 2010).…”

“…In other, non-axisymmetric, vortex-shedding configurations, no limit on the growth or size of vortices is known. In the case of vortex formation from two-dimensional orifices, for example, recent experimental (Afanasyev 2006) and computational (Pedrizzetti 2010) results suggest that there is no limit on the growth of a vortex dipole.…”

Nested contour dynamics models for axisymmetric vortex rings and vortex wakes

“…Given that these vortices have been used to model vortex rings al different stages in their growth, this change in response suggests that the perturbation response of models for isolated vortex rings could be a useful tool in understanding the pinch-off of vortex rings in real flows. Since pinch-off was not expected to occur in two dimensions (Afanasyev 2006; Pedrizzetti 20 I 0), this conjecture was supported by the fact that no such change in response was observed when we considered perturbations to a two-dimensional analogue to the Norbury family of vortex rings, namely the Pi errehumbert fam ily of vortex dipoles (Pierrehumbert 1980). However, the vortex rings and dipoles considered in O'Farrell & Dabiri (2012) consisted of single patches inside which the vorticity was constant (in the twodimensional case) or a linear function of the distance from the axis of symmetry (i n the axisymmetric case).…”

Pinch-off of axisymmetric vortex pairs in the limit of vanishing vortex line curvature

“…Unlike the axisymmetric case, both studies found that vortex dipoles continue to accept vorticity throughout the formation process and no pinch-off from the generating jet was observed. The experiments of Afanasyev 6 were in the Reynolds number range 50-450, allowing for the possibility that viscous diffusion may have obscured the pinch-off process, but Pedrizzetti's results 3 were at a higher Reynolds number. O'Farrell and Dabiri 7 studied the perturbation response of the Pierrehumbert and Norbury families of vortex dipoles and rings, respectively.…”

“…3,4 The similarity between vortex dipoles and axisymmetric vortex rings suggests that the formation of vortex dipoles may be subject to a growth limiting mechanism similar to the pinch-off process for axisymmetric vortex rings identified by Gharib et al 5 A number of recent studies have investigated this possibility. Afanasyev 6 and Pedrizzetti 3 studied the formation of 2D vortex dipoles from transient jets experimentally and numerically, respectively. Unlike the axisymmetric case, both studies found that vortex dipoles continue to accept vorticity throughout the formation process and no pinch-off from the generating jet was observed.…”