THE ANALYSIS OF FORMING THE BULGE IN A SPILLING WATER-WAVE

The early stages of a spilling breaking water wave leading to the form ation of a bulge on the forward face of the wave are investigated. In this study, simultaneous space-time measurements of the free-surface e levation of a spilling breaking water wave are recorded and analyzed. The analysis, carried out in the frame of reference moving with the cr est of the wave, reveals that the formation of the bulge is due to the presence of a shock-like mode. In the previous frame of reference, th e shock itself is unsteady but its (spatial) location is time independ ent and coincides with the ''toe'' of the bulge. As time increases, th e shock undergoes a flip (a reflection symmetry) with respect to the m idpoint of our time interval. Such a flip is responsible for an abrupt increase of the wave steepness, which will lead to wave breaking at l ater times. Following these observations, we present a two-dimensional quantitative model which reproduces both the formation of the bulge a nd the sudden increase of the wave steepness.