1. Wave Shoaling Schematic Changes that occur when a wave shoals (moves into shallow water): In deep water = profile of swell is nearly sinusoidal. Enter shallow water, waves undergo a systematic transformation. Wave velocity and wave length decrease while the wave height increases. Only wave period remains constant.

2. Wave Shoaling – L & C Deep water - L, C depend only on period Shallow water - L, C depend only on the water depth Summarize regions of applications of approximations Behavior of normalized variables.

3. P in P out Outside the surf zone P in = P out Wave energy flux is conserved Ecn = constant Ecn = E ∞ c ∞ n ∞  ∞ =((1/2n)(C ∞ /C)) 1/2 Wave Shoaling – H Explains why orthogonally directed waves increase height during shoaling Direct compensation for slowing of individual waves and need to maintain constant wave energy flux Waves convert a significant fraction of their kinetic energy to potential energy

4. Wave Shoaling – Steepness (H/L) Straightforward consequence of combined shoaling behavior of H & L. Steepness initially decreases upon entry to intermediate water depth, then rapidly increases until instability condition associated with wave breaking.

5. Wave Refraction Photos

6. Wave Refraction: Wave Crests vs. Wave Rays Wave crests are the line segments that connect the peaks (or troughs) of a wave field. The crests are visible to the observer. Wave rays are the lines orthogonal (perpendicular) to the wave crests, which represent the direction of wave propagation

7. Wave Refraction Wave Refraction - Point Reyes

8. c = (gh) 1/2 Snell’s Law Wave Refraction

9. Wave Refraction: Energy flux per unit length of wave crest Energy flux per unit length of wave crest is not necessarily conserved Can lead to a decrease in wave height during the shoaling and refraction process.

10. Wave Refraction - La Jolla Canyon

11. Combined Refraction and Shoaling

12. Effect of Shoaling H = 2 m T = 10 s othogonal angle of incidence

13. Effect of Shoaling and Refraction H = 2 m T = 10 s compare: orthogonal wave vs. refracting wave

14. Modeling refraction - wave rays H = 2 m T = 10 s  = 270˚

15. Modeling refraction - wave rays - double period H = 2 m T = 20 s  = 270˚

16. bathymetry (in feet) focusing waves “Jaws” Surfing Reef, Maui Model simulations of individual waves - not time averaged.

17. Wave Diffraction Lateral translation of energy along a wave crest. Most noticeable where a barrier interrupts a wave train creating a "shadow zone". Energy leaks along wave crests into the shadow zone. Also by analogy to light, Huygen's Principle explains the physics of diffraction through a superposition of point sources along the wave crest.

18. Wave Diffraction- Barcelona

19. Modeling with SWAN Ref/Diff numerical simulation of shoaling and refraction - monochromatic (not spectral - boo.) SWAN - used here at UF (spectral - yay.)