Global instability analysis and experiments on buoyant plumes

Abstract

The present work investigates the puffing instability of circular buoyant plumes by performing global linear stability analysis and experiments. In the non-dimensional parameter space investigated, plumes exhibit global instability only for axisymmetric perturbations with two unstable modes, which are of oscillatory type. The frequencies of these two unstable global modes agree well with the experiments which suggest that puffing occurs in buoyant plumes as a result of linear global instability. A comprehensive investigation on the effect of various non-dimensional parameters and inlet velocity profiles on frequency and growth rates of the global modes is carried out. The results are used to delineate the stability boundaries for these global modes and to obtain scaling laws for the associated oscillation frequencies. The analysis demonstrates that the two buoyancy parameters, Froude number and source-to-ambient density ratio, play dominant roles in impacting plume transition and oscillation frequencies. Results from global linear stability analysis and earlier experiments have majorly differed in two aspects. The earlier experiments reported a switch in puffing frequency scaling in Richardson number range 100–500, while the instability analysis predicts this switch at around 6000. Also, the instability analysis predicts the occurrence of puffing at density ratios higher than the critical value 0.5–0.6 reported in earlier experiments. To address these differences and validate the results obtained from global linear stability analysis, experiments are performed in a set-up that has been carefully designed to minimize the settling chamber disturbances. The present experiments corroborate the findings of global linear stability analysis. The mechanisms responsible for global instability in plumes have been identified using perturbation vorticity transport equation.