Height and stability of laminar plane fountains in a homogeneous fluid

The behaviour of plane fountains, resulting from the injection of a denser fluid upwards into a large body of a lighter homogeneous fluid, is investigated numerically. The transient behaviour of fountains with a uniform inlet velocity, Reynolds number Re = 100, Prandtl number Pr = 7, and Froude number 0.25 ⩽ Fr ⩽ 10.0 is studied numerically. In the present case, the density variation is as a result of temperature difference between the fountain and the ambient fluids. Three distinct regimes are identified; steady and symmetric fountains for 0.25 ⩽ Fr ⩽ 2.0, unsteady fountains with periodic lateral oscillation for 2.25 ⩽ Fr ⩽ 3.0, and unsteady fountains with aperiodic lateral oscillations for Fr ⩾ 4.0. It is found empirically that the non-dimensional fountain height, zm, scales differently with Froude number in each of these regimes; in the steady and symmetric region zm∼Fr, in the unsteady and periodic lateral oscillation region zm∼Fr1.15 and in the unsteady and aperiodic lateral oscillation region zm∼Fr4/3. The results are compared with previous numerical and experimental results, where available and are consistent.