Unstable waves on an axisymmetric jet column

Abstract

The growth of infinitesimal disturbances on an axisymmetric jet column is investigated theoretically and experimentally. The theoretical analysis is based upon inviscid stability theory, wherein axisymmetric, helical and double helical disturbances are considered from the spatial reference frame. In the jet flow field near the source, the mean velocity profile is observed to have a potential core and a thin, but finite, shear layer between the potential core and the quiescent ambient fluid. With downstream distance, the potential core diameter decreases and the shear-layer thickness increases. To incorporate these variations into the theory, a quasi-uniform assumption is adopted, whereby successive velocity profiles are analysed individually throughout the region in the jet flow where disturbances are observed to be small. The results of the theory indicate that initially, in the jet flow where the shear layer is thin and the potential core is larger, all disturbances considered are unstable. The dominant disturbance in the jet is an axisymmetric one. However, further downstream in the jet, where the half-breadth thickness of the shear layer is 55% of the potential core radius, a helical disturbance is found to dominate the axisymmetric and double helical modes. Nowhere in the jet flow field examined was the double helical disturbance found to be dominant. The cross-stream distributions of velocity and vorticity for the dominant disturbance modes are presented according to the spatial stability theory.

The downstream development of the jet column and the characteristics of the disturbances amplifying on it were also studied in a water tank. No artificial stimulation of any particular disturbance was used. The experimental results show good agreement with the results of the theory in the region where the disturbances are small. However, conclusive confirmation of the switch in the hierarchy of dominant disturbances was not found. Half of the time the disturbance observed experimentally exhibits an axisymmetric character and the other half a helical one. This apparently is due to the similar spatial amplification rates experienced by both of these disturbance modes. It is concluded that this switching of dominant modes is, in large part, responsible for (i) the well-known natural drifting of disturbance characteristics in jet flows, and (ii) the wide variety of observations made in previous jet experiments.