1. Freak Waves in Shallow Water Josh Moser & Chris Wai

2. Rogue waves are being reported more and more in today’s world.

6. The dispersion relation describes the physics of the waves,

7. The spread of the waves is then dependent on the wavelength as shown in k, the wave number. To create a freak wave, it is thought of having the exact dispersion relation in which multiple waves meet up at some time and space, generating a freak wave.

8. The Korteweg-de Vries equation is a nonlinear, partial differential equation that has applications to water waves

9. Small-amplitude waves in shallow water is a statement of weak nonlinearity

11. Plugging into the linearized KdV equation to find the ordinary differential equation

15. So now we have an equation that looks like an Airy Integral

16. Now we can make simple substitutions to exploit what is known

17. We know that this is in the form of the Airy Integral using slow time and slow space scales

18. Substitutions can be made to convert it back to real time and space scales for the wavemaker

20. Now consider different initial conditions

32. How do we generate these waves?

33. Mass flux

40. In conclusion Lot’s of differential equations Very mathy Had a lot of fun

41. Things to do next and new questions to ask Find numerical solution and try to replicate results See how the data can be used to predict freak waves that may come into the coast Find how the sea in real life translates to boundary and initial conditions Find the set of the conditions that cause freak waves at the shore Predict and “control” Save lives

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