Foam patches behind spilling breakers

Abstract

Previous theoretical and laboratory studies of spilling breakers on a beach are described and discussed, paying particular attention to models that emphasize the importance of air bubbles in the spill. At first such a spill forms at a sharp crest, and accelerates down the front of the wave as it propagates towards the shore. Then the crest becomes more rounded and this allows part of the aerated water to flow backwards over or under the crest, leaving a foam patch behind. Laboratory experiments in channels of constant width have documented many features of these flows. But recent new observations on gently sloping beaches have revealed another three-dimensional phenomenon, which is not possible in laboratory channels, and which has rarely been described or properly explained. Initially the spill forms nearly simultaneously over a wide front and extends down the forward face of the wave. Then at some point on the spill some of the foam flows over the crest and is left behind in a continuous patch of increasing length. At the same time the rounded portion of the crest propagates sideways in both directions, as the shear flow at its edge entrains fluid from the sharp crests on either side. This leads to a patch that is triangular in shape, with a peak directly behind the initial instability and of zero length where the backward flow has just begun. This idea has been quantitatively tested using selected photos taken from a headland above a beach, rectified to produce plan views. The patches are indeed triangular, sometimes distorted by a shear flow parallel to the wave crest but with a narrow range of peak angles, and on this beach which has a very uniform slope there is no systematic dependence on other parameters such as the wave height at breaking or the bathymetry conditions.