T. van den Bremer, Wave breaking and jet formation on axisymmetric surface gravity waves

Axisymmetric standing waves occur across a wide range of free surface flows. When these waves reach a critical height
(steepness), wave breaking and jet formation occurs. For travelling surface gravity waves, the process of wave breaking 
is generally considered to limit wave height and reversible wave motion. In the ocean, the behaviour of directionally 
spread waves lies between the limits of purely travelling (2D) and axisymmetric (3D). Hence, understanding wave breaking 
and jet formation on axisymmetric surface gravity waves is an important step in understanding extreme and breaking waves 
in the ocean. We examine an example of axisymmetric wave breaking and jet formation colloquially known as the ‘spike wave’, 
created in the FloWave circular wave tank at the University of Edinburgh, UK. We generate this spike wave with maximum crest
amplitudes of 0.15-6.0 m, with wave breaking  occurring  for crest amplitudes  greater than 1.0 m.  Unlike 2D travelling 
waves, wave breaking does not limit maximum crest amplitude, and our measurements approximately follow the jet height 
scaling proposed by Ghabacheet al. (2014, JFM) for cavity collapse. The spike wave is predominantly created by linear 
dispersive focusing, which forms a deep wave trough. This trough or cavity then collapses producing a jet, which is highly
sensitive to the trough’s shape. The evolution of the jets that forming our experiments is predicted well by the hyperbolic 
jet model proposed by Longuet-Higgins (1983, JFM), previously applied to jets forming on bubbles at much smaller scale