Around the cusp singularity and the breaking of waves

Abstract

We record the breaking of water waves focusing at the Huygens Cusp of a parabolic wave maker using a fast video camera at a rate of 2000 images per second. The movie shows the very early time of the water tongue plunging ahead of the wave crest. Soon after, some capillarity wavelets are clearly visible. The image analysis of these space time data permits the measurement of the expected 3/2 power of time law as dictated by the cusp singular geometry given by the Catastrophe Theory. To our knowledge this is the first time that this scaling law is measured from fluid dynamics videos.