1. Modeling Breaking Waves Zoe Boekelheide Scientific Computing April 30, 2003

2. Questions Qualitative #1: Can I model breaking waves? #2: Can I make waves that look like actual ocean waves? Quantitative #3: How do the time scales of waves of different amplitudes compare? #4: Can I calculate a variable to measure “surfability” of a wave?

3. The Model One-dimensional model Assumes deep water with zero viscosity Method borrowed from M.S. Longuet- Higgins and E.D. Cokelet, “The deformation of steep surface waves on water” Fourth-order Runge-Kutta solver

4. The Waves I picked a realistic wave profile to test, and tried it for 5 different ratios of amplitude to wavelength Amplitude/Wavelength.31.41.62.83 1.25

6. #1: Can I Model Breaking Waves? YES!

7. #2: Do they actually look like ocean waves?

9. Successes: The waves steepen over time like breaking ocean waves do. They break like ocean waves do. Failures: The “curl” doesn’t actually curl, it kind of just floats in the air.

10. #3: How do the time scales of waves of different amplitudes compare? The 5 waves I tested all had the same behavior, but on very different time scales.

11. Amplitude/ Wavelength Time scale (Δt).31.008.41.004.62.0015.83.0005 1.25.00033

13. #4: Can I calculate a variable to measure “surfability” of a wave? Simple rules for surfing: You can only surf on parts of a wave that make an angle between 0° and 35° with the horizontal You can only surf on a concave surface of a wave  Takeshi Sugimoto, ”How to Ride a Wave”

14. Define variable surfability Surfability = (distance along wave satisfying the simple surfing conditions) x (time scale) The surfability variable indicates only how much the wave is able to be surfed— not the quality of the surfing Now I can calculate a value for each of my five waves and compare.

15. Amplitude/ Wavelength Surfability.31.2944.41.1135.62.0310.83.0079 1.25.0033

17. Conclusions #1: I can model breaking waves! #2: But not perfectly… #3: Waves with different amplitudes have the same behavior, but over different time scales. Larger amplitude waves break faster. #4: Smaller amplitude waves are more surfable, probably because they last longer.