Size distributions of sprays produced by violent wave impacts on vertical sea walls

When a steep, breaking wave hits a vertical sea wall in shallow water, a flip-through event may occur, leading to the formation of an up-rushing planar jet. During such an event, a jet of water is ejected at a speed many times larger than the approaching wave's celerity. As the jet rises, the bounded fluid sheet ruptures to form vertical ligaments which subsequently break up to form droplets, creating a polydisperse spray. Experiments in the University of Hokkaido's 24 m flume measured the resulting droplet sizes using image analysis of high-speed video. Consideration of the mechanisms forming spray droplets shows that the number density of droplet sizes is directly proportional to a power p of the droplet radius: where p=-5/2 during the early break-up stage and p=-2 for the fully fragmented state. This was confirmed by experimental observations. Here, we show that the recorded droplet number density follows the lognormal probability distribution with parameters related to the elapsed time since the initial wave impact. This statistical model of polydisperse spray may provide a basis for modelling droplet advection during wave overtopping events, allowing atmospheric processes leading to enhanced fluxes of mass, moisture, heat and momentum in the spray-mediated marine boundary layer over coasts to be described.