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 image, in the unsteady and periodic lateral oscillation region image and in the unsteady and aperiodic lateral oscillation region image. The results are compared with previous numerical and experimental results, where available and are consistent.