Onset of asymmetry and three-dimensionality in transitional round fountains in a linearly stratified fluid

Fountains injected into stratified fluids are widely found in nature and engineering settings. The onset of asymmetry, three dimensionality and entrainment which occurs in transitional fountains is the key to shed light on the turbulence generation mechanism in fountains. It is also apparent that the stratification of the ambient fluid has significant effects on the onset of asymmetry, three-dimensionality and entrainment in fountains and a study on such effects will provide further insight into the interaction between stratification and turbulence generation mechanism in fountains. In this study, a series of direct numerical simulations were carried out for transitional round fountains in the ranges of 1=200, the Fr = 2 fountains maintain axisymmetry only in the developing stage and become asymmetric and threedimensional at fully developed, steady state, and the stratified case has in general stronger extents of asymmetry and threedimensionality than the homogeneous case; when Fr>=2, the fountains at Re = 200 maintain axisymmetry only in the developing stage and become asymmetric and three-dimensional at fully developed, steady state, and the stratified case has much stronger extents of asymmetry and three-dimensionality than the homogeneous case; The occurrence of asymmetry and three-dimensionality becomes much earlier when Re or Fr increases