Weak fountains in a stratified fluid

The behavior of weak axisymmetric and plane fountains resulting from the injection of denser fluid upwards into large containers containing a stably stratified fluid has been explored using dimensional analysis, scaling analysis, and direct numerical simulation. For weak fountains, with Froude number Fr approximately 1.0, dimensional and scaling analyses have been used to derive scaling relations for the dimensionless fountain height, width, thickness of the temperature layer, and development times in terms of the Froude number Fr, Reynolds number Re, Prandtl number Pr, and ambient stratification number s. Numerical simulations have been carried out for a series of Fr, Re, Pr, and s for both axisymmetric and plane fountains to validate and quantify the scaling relations obtained by the dimensional and scaling analyses. The numerical results have been found to agree well with the analytical scaling relations.