Wave Transformation Mazen Abualtayef Associate Prof., IUG, Palestine Wave Transformation Wave transformation describes what happens to waves as they travel from deep into shallow water

Diffraction Shoaling Deep Refraction Shallow

Wave Transformation Wave transformation is concerned with the changes in H, L, C and , 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.

Shoaling b0 H0 H E is the wave energy density

Ks is the shoaling coefficient Coastline 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 Wave refraction

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 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 Another way to calculate Kr using the wave direction of propagation by Snells Law 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 0=30. Calculate H and in 10m and 2m of water depth. Answer: L0 = gT2/2 = 100m For 10m depth: d/L0 = 0.10 and from wave table,

d/L = 0.14, Tanh(kd) = 0.71 and Ks = 0.93 = 20.9 Kr = 0.96 H = 2.70 m n = 0.81 Wave breaking

Wave shoaling causes wave height to increase to infinity in very shallow water as indicated in Fig. 7.1. 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. 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). 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) Example 7.2 - RSB spreadsheet Refraction-Shoaling-Breaking 6.00 Wave Height (m)

5.00 H (rs) Hb (H/L) (H/d) (7.32) Hb (d/L) 4.00

3.00 2.00 1.00 0.00 0.00 5.00 Depth (m)

10.00 15.00 For this example with the beach slope m=0.02, Hb=2.9m (Eq. 7.32) with b=15.34, in a depth of water of 4.9 m. Problem

Given: T=10 sec, H0=4 m, 0=60 Find: H and at the depth of d =15.6 m Check if the wave is broken at that depth Assume b 0.78 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. Wave diffraction Propagation of a wave around an obstacle Wave diffraction Wave diffraction Semi infinite rigid impermeable breakwater

Through a gap Wave diffraction 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. 7.10.

Wave diffraction Wave diffraction When shoaling, refraction and diffraction all take place at the same time, wave height may be calculated as Wave reflection H r Cr .H i

2 r aI Cr 2 b Ir m

Ir H i / L0 Reflection The Wedge, Newport Harbor, Ca Wave energy is reflected

(bounced back) when it hits a solid object. waves