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-off) 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 time) 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.