Around the cusp singularity and the breaking of waves

TL;DR

This study captures the early stages of water wave breaking at a cusp singularity using high-speed video, confirming the theoretical 3/2 power law predicted by Catastrophe Theory in fluid dynamics.

Contribution

First experimental measurement of the 3/2 power law scaling at a water wave cusp using high-speed imaging and image analysis.

Findings

Confirmed the 3/2 power law scaling in wave cusp singularity

Captured early wave breaking dynamics with high temporal resolution

Provided empirical evidence linking fluid dynamics to Catastrophe Theory

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.