Vertical Plane Buoyant Jets and Fountains in a Uniform Stagnant Ambient Revisited

Planar, vertical buoyant jets are of particular interest, both for research and practical purposes for being related to the disposal of the effluent from wastewater treatment plants or saline, a by-product from desalination plants into a body of stagnant fluid. Analytical, closed form solution is derived for plane buoyant jets based on a buoyant jet width parameter proposed by List and Imberger (1973), and compares to earlier laboratory experiments satisfactorily. The derived entrainment coefficient as a function of the local Richardson number of the flow, takes two asymptotic values for jet-like and plume-like flows, while in fountains it takes values lower than that in jets. Laboratory experiments were performed to measure the penetration height of vertical plane fountains with initial Froude number in the range 20 to 130 using shadowgraph and Planar Laser Induced Fluorescence (PLIF) techniques. Interest was focused on the maximum and terminal, steady-state penetration height before the flow direction reversed. The flow was found to be in a state of unstable equilibrium, as it deviated from the vertical axis, swinging on either side. The equations of motion have been solved numerically using the derived entrainment coefficient function, and the results are congruent to earlier and present experiment for vertical fountains.