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Wave Transformation Coastal & Marine Environment Coastal & Marine Environment Chapter 7 Wave Transformation Mazen Abualtayef Assistant Prof., IUG, Palestine Coastal & Marine Environment Wave Transformation Chapter Wave transformation describes what happens to 7 waves as they travel from deep into shallow water Diffraction Shoaling Deep Refraction Shallow Coastal & Marine Environment Wave Transformation Wave transformation is concerned with the Chapter changes in H, L, C and a, the wave angle with the bottom contours; wave period T 7 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. Coastal & Marine Environment Shoaling b0 H Chapter 0 7 H E is the wave energy density Coastline Ks is the shoaling coefficient Coastal & Marine Environment Wave refraction Chapter • As waves approach shore, the part of the wave in shallow water slows 7 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 Coastal & Marine Environment Wave refraction Chapter 7 Coastal & Marine Environment Wave refraction Chapter 7 We can now draw wave rays (lines representing the direction of wave propagation) perpendicular to the wave crests and these wave rays bend Coastal & Marine Environment Wave refraction When the energy flux is conserved between the wave Chapter rays, then 7 where b is the distance between adjacent wave rays. Kr is the refraction coefficient Coastal & Marine Another way to calculate Kr using the wave direction of Environment propagation by Snell’s Law Chapter 7 Coastal & Marine Environment Example 7.1 Simple Refraction-Shoaling Calculation Chapter A wave in deep water has the following characteristics: H0=3.0 m, T=8.0 sec and a =30°. Calculate H and a in 10m and 2m of 7 0 water depth. Answer: 2 L0 = gT /2π = 100m For 10m depth: d/L0 = 0.10 and from wave table, d/L = 0.14, Tanh(kd) = 0.71 and n = 0.81 Ks = 0.93 a = 20.9° Kr = 0.96 H = 2.70 m Coastal & Marine Environment Chapter 7 Coastal & Marine Environment Wave breaking Wave shoaling causes wave height to increase to Chapter 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 7 breaks and dissipates its energy. Wave heights are a function of water depth, as shown in Fig. 7.7. Coastal & Marine Environment Wave breaking Chapter Wave shoaling, refraction and diffraction 7 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). Coastal & Marine Environment Wave breaking Chapter The breaker type is a function of the beach 7 slope m and the wave steepness H/L. Miche, 1944 b = 0.78 McCowan, 1894; Munk, 1949 Kamphuis,1991 (7.32) Coastal & Marine Environment Example 7.2 - RSB spreadsheet Chapter Refraction-Shoaling-Breaking 6.00 75.00 H (rs) Hb (H/L) 4.00 Hb (d/L) 3.00 2.00 Wave Wave Height (m) 1.00 0.00 0.00 5.00 10.00 15.00 Depth (m) For this example with the beach slope m=0.02, Hb=2.9m (Eq. 7.32) with ab=15.3°, in a depth of water of 4.9 m. Coastal & Marine Environment Problem Chapter Given: T=10 sec, H0=4 m, a0=60° 7 Find: H and a at the depth of d =15.6 m Check if the wave is broken at that depth Assume b 0.78 Coastal & Marine Environment Wave diffraction Chapter Wave diffraction is concerned with the transfer of wave energy across wave rays. Refraction 7 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. Coastal & Marine Environment Wave diffraction Propagation of a wave around an obstacle Chapter 7 Coastal & Marine Environment Wave diffraction Chapter 7 Coastal & Marine Environment Wave diffraction Chapter • Semi infinite rigid impermeable breakwater 7 • Through a gap Coastal & Marine Environment Wave diffraction Chapter 7 Coastal & Marine Environment Wave diffraction The calculation of wave diffraction is quite complicated. For preliminary calculations, however, it is often sufficient to use diffraction templates. One such Chapter template is presented in Fig. 7.10. 7 Coastal & Marine Environment Wave diffraction Chapter 7 Coastal & Marine Environment Wave diffraction Chapter 7 When shoaling, refraction and diffraction all take place at the same time, wave height may be calculated as Coastal & Marine Environment Wave reflection Chapter HCH . 7 r r i 2 aIr m CIrr2 bI r HLi / 0 Coastal & Marine The Wedge, Newport Harbor, Ca Environment Reflection Chapter Wave energy is reflected 7 (bounced back) when it hits a solid object. waves Coastal & Marine Environment Summary Chapter What can affect the way that waves travel? Wave refraction: the slowing and bending of 7 waves in shallow water. Wave diffraction: propagation of a wave around an obstacle. Wave reflection: occurs when waves “bounce back” from an obstacle they encounter. Reflected waves can cause interference with oncoming waves, creating standing waves. Standing waves: are found in inlets and bays They remain in a fixed position.
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