Overturning in a filling box

Overturning in a cylindrical filling box driven by a turbulent plume is examined theoretically and experimentally. We establish the initial penetration depth (h) of the buoyant flow that intrudes vertically up the sidewall as a function of the box radius (R) and height (H). Dimensional arguments reduce the problem to finding eta = h / H as a function of the aspect ratio Phi = R/H. The flow is modelled in two parts, the radial outflow from the plume along the base of the box and the flow up the sidewall. The outflow is modelled as a forced radial gravity current with constant buoyancy flux while the sidewall flow is modelled as a line fountain. Two regimes were found: first, when the plume outflow is adjusting toward a pure gravity current on impact with the vertical wall and the rise height is given by eta similar to Phi(-1/3) ; secondly, when the outflow is fully developed on, or before, impact and the rise height is given by eta similar to Const. Experimental results show good agreement with these scalings and allow the constants of proportionality to be established.