The temporal stability of a developing jet: a model problem

Abstract

AbstractThe temporal instability of a developing swirling incompressible jet is considered. The jet development (in the streamwise direction) is modelled by combining a near-field and far-field approximation to the jet velocity profile into a one parameter family of basic velocity fields. The single parameter in the jet velocity field then allows us to model the radial spreading of the jet and the decay of swirl observed experimentally. Two distinct modes of instability of this model profile are found. The first is that found from a stability analysis of a fully developed swirling jet in the far field whilst the second is relevant to a “top-hat” jet with an imposed rigid body rotation. We demonstrate that the effect of azimuthal swirl is to destabilise both modes of instability. Additionally our results suggest that the near-nozzle modes of instability will dominate; indeed the growth rates of these modes are significantly larger than those found from previous studies of a fully developed jet in the far-field region.