1. Mazen Abualtayef Associate Prof., IUG, Palestine
Wave Transformation
Mazen Abualtayef Associate Prof., IUG, Palestine

2. Wave Transformation
Wave transformation describes what happens to waves as they travel from deep into shallow water
Diffraction
Shoaling
Deep
Refraction
Shallow

3. Wave Transformation
Wave transformation is concerned with the changes in H, L, C and a, the wave angle with the bottom contours; wave period T remains constant throughout the process. To derive the simpler solutions, wave transformation is separated into wave refraction and diffraction. Refraction is wave transformation as a result of changes in water depth. Diffraction is specifically not concerned with water depth and computes transformation resulting from other causes, such as obstructions. Discussions about wave refraction usually begin by calculating depth related changes for waves that approach a shore perpendicularly. This is called wave shoaling.

4. Shoaling b0 H0 H E is the wave energy density Coastline
Ks is the shoaling coefficient
Coastline

5. Wave Refraction
As waves approach shore, the part of the wave in shallow water slows down
The part of the wave in deep water continues at its original speed
Causes wave crests to refract (bend)
Results in waves lining up nearly parallel to shore
Creates odd surf patterns

6. Wave refraction

7. Wave refraction
We can now draw wave rays (lines representing the direction of wave propagation) perpendicular to the wave crests and these wave rays bend

8. Wave refraction
When the energy flux is conserved between the wave rays, then
where b is the distance between adjacent wave rays.
Kr is the refraction coefficient

9. Another way to calculate Kr using the wave direction of propagation by Snell’s Law

10. Simple Refraction-Shoaling Calculation
Example 7.1
Simple Refraction-Shoaling Calculation
A wave in deep water has the following characteristics: H0=3.0 m, T=8.0 sec and
a0=30°. Calculate H and a in 10m and 2m of water depth.
Answer:
L0 = gT2/2π = 100m
For 10m depth:
d/L0 = 0.10 and from wave table,
d/L = 0.14, Tanh(kd) = and n = 0.81
 Ks = 0.93
 a = 20.9°
 Kr = 0.96
 H = 2.70 m

12. Wave breaking
Wave shoaling causes wave height to increase to infinity in very shallow water as indicated in Fig There is a physical limit to the steepness of the waves, H/L. When this physical limit is exceeded, the wave breaks and dissipates its energy. Wave heights are a function of water depth, as shown in Fig. 7.7.

13. Wave breaking
Wave shoaling, refraction and diffraction transform the waves from deep water to the point where they break and then the wave height begins to decrease markedly, because of energy dissipation. The sudden decrease in the wave height is used to define the breaking
point and determines the breaking parameters (Hb, db and xb).

14. Wave breaking
The breaker type is a function of the beach slope m and the wave steepness H/L.
Miche, 1944 =
McCowan, 1894; Munk, 1949
Kamphuis,1991
(7.32)

15. Example 7.2 - RSB spreadsheet
(H/d)
(7.32)
For this example with the beach slope m=0.02, Hb=2.9m (Eq. 7.32) with ab=15.34°, in a depth of water of 4.9 m.

16. Problem Given: T=10 sec, H0=4 m, a0=60°
Find: H and a at the depth of d　=15.6 m
Check if the wave is broken at that depth
Assume
L0 = gT2/2π = 156m
For 15.6m depth:
d/L0 = 0.10 and from wave table,
d/L = 0.14, Tanh(kd) = and n = 0.81
 Ks = 0.93
 a = 37.9°
 Kr = 0.80
 H = 2.96 m
H/d = 0.74 < 0.78 no breaking

17. Wave diffraction
Wave diffraction is concerned with the transfer of wave energy across wave rays. Refraction and diffraction of course take place simultaneously. The only correct solution is to compute refraction and diffraction together using computer solutions. It is possible, however, to define situations that are predominantly affected by refraction or by diffraction. Wave diffraction is specifically concerned with zero depth change and solves for sudden changes in wave conditions such as obstructions that cause wave energy to be forced across the wave rays.

18. Wave diffraction
Propagation of a wave around an obstacle

19. Wave diffraction

20. Wave diffraction Semi infinite rigid impermeable breakwater
Through a gap

21. Wave diffraction

22. Wave diffraction
The calculation of wave diffraction is quite complicated. For preliminary calculations, however, it is often sufficient to use diffraction templates. One such template is presented in Fig

23. Wave diffraction

24. Wave diffraction
When shoaling, refraction and diffraction all take place at the same time, wave height may be calculated as

25. Wave reflection

26. Reflection
The Wedge, Newport Harbor, Ca
waves
Wave energy is reflected (bounced back) when it hits a solid object.