Modeling Breaking Waves Zoe Boekelheide Scientific Computing April 30, 2003
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?
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
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
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.
#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.
#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”
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.
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.