06 wave transformation

WAVE TRANSFORMATION Wave Transformation • Shoaling • Refraction • Diffraction • Reflection • Breaking • Reforming Wave Shoaling Wave Refraction Wave Refraction Wave Crests and Orthogonals (Rays) Refraction of Wave Rays Basic Presumption: Wave energy flux conserved between P0 rays P0 = P1 P1 Wave Energy Flux Conservation P  EC g b From point to 1: In deep water: Po  Eo Co bo P   ECg b    ECg b  Cg H1  H0 Cg 1 b0 1 Co  b1 2n C bo  KS K R b Shoaling coefficient Refraction coefficient Equivalent Deepwater Wave Height Ho’ : wave height in deep water if the wave is not refracted H 1 Co  Ho 2n C bo  KS K R b H0´ H0 Inkludera fig H H' KR  o Ho KS  H H o' Example, page 2-27: GIVEN: A deepwater oscillatory wave with a wavelength Lo=156 m, a height Ho=2 m, and a celerity Co=15.6 m/s, moving shoreward with its crest parallel to the depth contours Any effects due to reflection from the beach are negligible FIND: a Derive a relationship between the wave height in any depth of water and the wave height in deep water b Calculate the wave height when the depth is m c Determine the rate at which energy is transported toward the shoreline and the total energy delivered to the shore in hr Snell’s Law Snell’s Law Refraction: sin 1  sin  L1 C  sin  L2 C2 Wave ray spacing: b1 cos 1  b2 cos 2 Example, page 2-64: GIVEN: The wave angle o=30 deg, and the period and depth are such that C/Co=0.5 FIND: Wave angle at that depth and refraction coefficient Example, Refraction Calculation C0 = 1.56T = 7.8 m/s, L0 = 1.56T = 39 m d 25 12 H3 = ? , α3 = ? d/L0 0.64 0.31 0.077 C/C0 0.99 0.97 0.64 C 7.79 ~ C0 7.56 5.01 d=3m d = 12 m d = 25 m Wave gage * α25 = 28 o H0 = m, T = sec, α = 28o Example, Refraction Calculation C0 = 1.56T = 7.8 m/s, L0 = 1.56T = 39 m d 25 12 H3 = ? , α3 = ? d/L0 0.64 0.31 0.077 C/C0 0.99 0.97 0.64 C 7.79 ~ C0 7.56 5.01 d=3m d = 12 m α’25 = 17 o (measured) d = 25 m Wave gage * α25 = 28 o H0 = m, T = sec, α = 28o Example, Refraction Calculation C0 = 1.56T = 7.8 m/s, L0 = 1.56T = 39 m d 25 12 H3 = ? , α3 = ? d/L0 0.64 0.31 0.077 C/C0 0.99 0.97 0.64 ’ C12 /C25 sinα12 = sinα25 C 7.79 ~ C0 7.56 5.01 α12 = 16.6o draw! d=3m d = 12 m α’25 = 17 o (measured) d = 25 m Wave gage * α25 = 28 o H0 = m, T = sec, α = 28o Example, Refraction Calculation C0 = 1.56T = 7.8 m/s, L0 = 1.56T = 39 m d 25 12 H3 = ? , α3 = ? d/L0 0.64 0.31 0.077 C/C0 0.99 0.97 0.64 ’ C12 /C25 sinα12 = sinα25 C 7.79 ~ C0 7.56 5.01 α12 = 16.6o draw! d=3m d = 12 m α12 = 16.6 o α’25 = 17 o (measured) d = 25 m Wave gage * α25 = 28 o H0 = m, T = sec, α = 28o Example, Refraction Calculation C0 = 1.56T = 7.8 m/s, L0 = 1.56T = 39 m d 25 12 H3 = ? , α3 = ? d/L0 0.64 0.31 0.077 C/C0 0.99 0.97 0.64 ’ C12 /C25 sinα12 = sinα25 C 7.79 ~ C0 7.56 5.01 α12 = 16.6o draw! d=3m α’12 = 25 o (measured) d = 12 m α12 = 16.6 o α’25 = 17 o (measured) d = 25 m Wave gage * α25 = 28 o H0 = m, T = sec, α = 28o Example, Refraction Calculation C0 = 1.56T = 7.8 m/s, L0 = 1.56T = 39 m d 25 12 H3 = ? , α3 = ? α’3 = 15.5 o (measured) d/L0 0.64 0.31 0.077 C/C0 0.99 0.97 0.64 ’ C12 /C25 sinα12 = sinα25 C 7.79 ~ C0 7.56 5.01 α12 = 16.6o draw! d=3m α3 = 16.2 o α’12 = 25 o (measured) d = 12 m α12 = 16.6 o α’25 = 17 o (measured) d = 25 m Wave gage * α25 = 28 o H0 = m, T = sec, α = 28o Example, Refraction Calculation C0 = 1.56T = 7.8 m/s, L0 = 1.56T = 39 m d 25 12 H3 = ? , α3 = ? d/L0 0.64 0.31 0.077 C/C0 0.99 0.97 0.64 C 7.79 ~ C0 7.56 5.01 b3 α’3 = 15.5 o (measured) ’ C12 /C25 sinα12 = sinα25 α12 = 16.6o draw! d=3m α3 = 16.2 o α’12 = 25 o (measured) d = 12 m α12 = 16.6 o α’25 = 17 o (measured) d = 25 m Wave gage * α25 = 28 o H0 = m, T = sec, α = 28o Example, Refraction Calculation C0 = 1.56T = 7.8 m/s, L0 = 1.56T = 39 m d 25 12 H3 = ? , α3 = ? α’’3 = 12.5 o (measured) b3 α’3 = 15.5 o (measured) d/L0 0.64 0.31 0.077 C/C0 0.99 0.97 0.64 ’ C12 /C25 sinα12 = sinα25 C 7.79 ~ C0 7.56 5.01 α12 = 16.6o draw! d=3m α3 = 16.2 o α’12 = 25 o (measured) d = 12 m α12 = 16.6 o α’25 = 17 o (measured) d = 25 m Wave gage * α25 = 28 o H0 = m, T = sec, α = 28o Example, Refraction Calculation C0 = 1.56T = 7.8 m/s, L0 = 1.56T = 39 m d 25 12 H3 = ? , α3 = ? α’’3 = 12.5 o (measured) b3 d/L0 0.64 0.31 0.077 C/C0 0.99 0.97 0.64 C 7.79 ~ C0 7.56 5.01 ’ C12 /C25 sinα12 = sinα25 α’3 = 15.5 o (measured) α12 = 16.6o draw! d=3m H3  H0Ks KR α3 = 16.2 o α’12 = 25 o (measured) K R  b25 / b3 d = 12 m α12 = 16.6 o H  1.35  0.96  2.60 m α’25 = 17 o (measured) d = 25 m Wave gage * K S  0.96 (Table 3)   (  3'   3'' ) /  14.0 o α25 = 28 o H0 = m, T = sec, α = 28o Fan-Type Refraction Diagram Main Items Understand and calculate: • kinetic and potential wave energy • wave energy flux and its conservation • refraction Diffraction Wave Diffraction Helmholtz equation: 2F 2 F   k 2F  x y Diffraction, Semi-Infinte Breakwater Diffraction Through a Gap Diffraction, Special Cases Wave approach in gap at an angle Diffraction, Special Cases Wave approach in gap at an angle 10 Diffraction, Special Cases B > 5L no interaction between tips Diffraction, Special Cases Diffraction around detached breakwater Superposition of diffraction sources K '  K L'2  K R'2  K L' K R' cos  11 .. .Wave Refraction Wave Refraction Wave Crests and Orthogonals (Rays) Refraction of Wave Rays Basic Presumption: Wave energy flux conserved between P0 rays P0 = P1 P1 Wave Energy Flux... K R b Shoaling coefficient Refraction coefficient Equivalent Deepwater Wave Height Ho’ : wave height in deep water if the wave is not refracted H 1 Co  Ho 2n C bo  KS K R b H0´ H0 Inkludera... negligible FIND: a Derive a relationship between the wave height in any depth of water and the wave height in deep water b Calculate the wave height when the depth is m c Determine the rate at