Maximum Vertical Penetration of Plane Turbulent Negatively Buoyant Jets

Series of plane turbulent negatively buoyant jet (or fountain) experiments were carried out by discharging saline water vertically upward from a rectangular slot into a stagnant fresh water environment. The plane jets were characterized by the formation of fronts that became unstable as the densimetric Froude number increased. When the Froude number was large (F> 10) the maximum penetration Z_m was mainly controlled by the momentum flux M_o and the buoyancy flux B_o, and the measurements confirmed that the asymptotic solution for large Froude numbers is Z_m=C_mb_oF^4/3, where b_o is the slot half-width, and the constant C_m= 2.0. At small Froude numbers, the maximum penetration was less than predicted by this asymptotic solution, and the deviations from this asymptotic solution were correlated using the mass flux Q_o and the buoyancy flux B_o. This correlation suggested that the virtual origin defined by the deviation from the large Froude number solution was located at a distance Z_q=C_qb_oF^2/3, with the constant C_q= 1.12. An attempt was made to explain large discrepancies in previous investigations.