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(m)b(o)F(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(q)b(o)F(2/3), with the constant C-q = 1.12. An attempt was made to explain large discrepancies in previous investigations.