Wave breaking and jet formation on axisymmetric surface gravity waves

Let me summarize the work we have just completed on axisymmetric surface gravity waves. After the presentation, there will be time for questions and feedback. Our study found that these waves can be much steeper than traveling Stokes waves. While there is a clear upper limit of 120 degrees for traveling Stokes waves, the maximum angle of axisymmetric standing waves is not a limiting angle. It is the beginning of the formation of vertical jets that follow the inertial model of Longuet-Higgins using these hyperbolic Lloyd shapes.

This physics is similar to what is observed for bubbles penetrating the surface and Faraday waves. Additionally, this mechanism could be responsible for the formation of taller waves than what is expected based on the uni-directional breaking threshold in crossing seas. We have been awarded funding to investigate this in more detail for the next 2.5 years in the wave breaking crossing seas project.

We are looking for students and postdocs to work with our collaborator Frederick Diaz to try and understand what happens in more realistic scenarios in crossing seas in terms of breaking and collaborate with experimentalists doing experiments both in Edinburgh and out in China. If you are interested, please email Frederick or myself.

During the Q&A section, Mario mentioned a classic paper by Zef. The first daughter is deaf in nature 2000, where they studied the feather wave collapsing cavity and showed that it is a self-similar process. Stephan asked if we tried to see if we match this particular self-similar scaling. We have read the paper and looked at the Longuet-Higgins work, but we must go back and look at it again.

There was also a discussion about the depression and micro rogue wave tremors associated with our work, but we haven't measured them yet. However, we do know that these pressures would penetrate down if things are crossing so deep. We are now building a gauge that has 100 gauges, so we can have spatial resolution and get things really precise. It was also mentioned that the probability of larger waves nearby is high, as seen with the drought planner wave.

Regarding the initiation of breaking, there is a clear explanation in the Longuet-Higgins paper. If we take Navier-Stokes and strip everything out, we just get a geometry problem that leads to infinite accelerations and velocities at some point.

In this conversation, the speakers discuss a research paper and the evidence they have found. The first speaker mentions that the other person could probably verbalize their findings more eloquently than they can, but they will send them the paper. The second person asks if they have seen any evidence of nonlinear focusing in the water they looked at. The first person responds that they have not found any evidence of it in the axisymmetric they studied. They thank each other and move on to another question.

The second person asks a more esoteric question about creating the conditions for the Drop FloWave and statistical theory. They mention that it is ambitious and like finding a needle in a haystack, but the first person agrees and mentions that they called their paper a case study. They have nothing to say about statistics and rogue waves and have removed the word roadway from the title of their paper. However, they believe that to say something about rogue waves, they must say something about statistics. The second person agrees and adds that spatial statistics must also be considered in crossing waves where the spatial statistics are no longer homogeneous because of the crossing.

Overall, the conversation revolves around their research paper and the findings they have made. They discuss the evidence they have found and the implications of their research.