Air entrainment and associated energy dissipation in steady and unsteady plunging jets at free surface

A theoretical formulation that describes energy transformation and dissipation caused by air bubble entrainment in water is proposed, in which the potential energy increase, induced by air bubble displacement and thermodynamical work done on air bubbles, are considered. Laboratory experiments were carried out with measurements of void fraction distributions under vertical steady plunging jets and plunging breakers of water waves. The energy dissipation rate has been estimated from measured data of void fractions and compared with the total energy dissipation rate. The ratios of energy dissipation rate caused by bubble entrainment to total dissipation rate have been found to be 4%–8% for vertical circular plunging jets and 36%–40% for plunging breakers.