Numerical and theoretical solutions of a turbulent Boussinesq fountain generated from maintained sources

This paper provides theoretical and numerical investigation carried out on a vertical up-flow model risen to investigate the jet maximum height based on buoyancy frequency parameter $\sigma_i$ and plume function $\Gamma_i$. We study the characteristic solution of the maximum height reached by the fountain through an asymptotic approach. Results show a discontinuity of affinity solution approximation at $\Gamma_i \gg 1$. The fluid became very negligible and ended with a fall back. The entrainment coefficient effect had no significant influence on the topological behavior profiles development of this jet with negative buoyancy force.