Transition to asymmetry of transitional round fountains in a linearly stratified fluid

In this study, a series of three-dimensional direct numerical simulations were carried out for transitional round fountains in a linearly-stratified fluid over the ranges of 100 ≤ Re ≤ 400, 1 ≤ Fr ≤ 8 and 0.0 ≤ s ≤ 0.3, where Fr, Re and s are the Froude, Reynolds, and dimensionless temperature stratification parameters, respectively, to examine, both qualitatively and quantitatively, the effect of these parameters on their transition to asymmetry and the asymmetric behavior. It is found that the transition to asymmetry are well represented and quantified by azimuthal velocity, with non-zero or noticeable azimuthal velocity indicating asymmetry. The results show that when Fr or Re are small, a fountain remains axisymmetric for all time; however, when Fr or Re are increased to be sufficiently large, the fountain will be axisymmetric initially, before becoming asymmetric and unsteady, ultimately reaching a fully developed quasi-steady stage when each quantity fluctuates over a constant, time-average, value. The stratification is found to play a positive role to stabilize the flow and to reduce or even to eliminate the asymmetric behavior. The numerical results were also used to develop the scaling for the time for transition to asymmetry, which is found to be strongly dependent on Fr and s, while only weakly dependent on Re.