Very weak fountains in a homogeneous fluid

The behaviour of very weak axisymmetric and plane fountains formed by the discharge of denser fluids upwards into large containers containing a homogenous fluid of lower density has been studied by dimensional analysis and direct simulations. For very weak fountains, the momentum fluxes are negligible compared with the buoyancy fluxes and the flows are governed by the balance between the buoyancy and the viscosity. Dimensional analysis shows that the fountain, fountain width, thickness of the temperature layer on the symmetry axis, and the times for the fountain flow in the fountain core to reach steady state and for the temperature layer to be fully developed are scaled by the Froude, Reynolds, and Prandtl numbers. These scalings have been validates and quantified by numerical simulations.