Direct simulation of transitional plane fountains in a homogeneous fluid

The fluid dynamics of transitional plane fountains with the Froude and Reynolds numbers in the ranges 1≤Fr≤6 and 100≤Re≤800 is investigated to examine the entrainment associated with the onset of turbulence. The direct numerical simulation results show that negligible entrainment occurs at the upflow-downflow interface for small Fr (<2) fountains, and only small entrainment on the downflow-ambient interface. However, entrainment occurs at both the upflow-downflow and the downflow-ambient interfaces for large Fr (>2) fountains, even at Re=100, with the extent of the entrainment increasing almost linearly with Re. The upflow and fountain widths show strong Re dependence and increase linearly with Fr, demonstrating that the onset of entrainment and instability occurs at relatively high Re (>1000) in small Fr (≤2) fountains, but at small Re (<100) in large Fr (>2) fountains.\u