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Transformation of Shallow-Water Waves

T he Certificate Program in Tsunami Science and Preparedness . Transformation of Shallow-Water Waves. Held at the University of Washington in Seattle, Washington (USA) , D uring July 21- August 2, 2007. T he Certificate Program in Tsunami Science and Preparedness .

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Transformation of Shallow-Water Waves

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  1. The Certificate Program in Tsunami Science and Preparedness. Transformation of Shallow-Water Waves Held at the University of Washington in Seattle, Washington (USA) , During July 21- August 2, 2007.

  2. The Certificate Program in Tsunami Science and Preparedness. The transformation of waves across the sea is a complex problem, including the processes of refraction, shoaling, breaking, energy dissipation by bottom friction, and reflection. As waves pass from deep water onto shallow water, the waves become highly nonlinear. Held at the University of Washington in Seattle, Washington (USA) , During July 21- August 2, 2007.

  3. The Certificate Program in Tsunami Science and Preparedness. Wave energy is dissipated due to breaking, but energy is also transferred to both higher and lower frequencies in the wave spectrum, and the spectral shape becomes flat Held at the University of Washington in Seattle, Washington (USA) , During July 21- August 2, 2007.

  4. The Certificate Program in Tsunami Science and Preparedness. Energy losses due to bottom friction are usually negligible in wave transformation across sandy beach profiles, but may be significant over shallow, rough reef flats where the bottom friction coefficient may be an order of magnitude larger than for a sandy bed. Held at the University of Washington in Seattle, Washington (USA) , During July 21- August 2, 2007.

  5. The Certificate Program in Tsunami Science and Preparedness. • Wave motion: Speed and energy • There are mathematical relationships linking the characteristics of wavelength (L), wave period (T) and wave height (H) to wave speed and to wave energy. • Wave speed  speed = distance/time • C = L/T (time one wavelength takes to pass a certain point) • Wave speed can also be represented by the equation: • Where: • g = acceleration due to gravity • L = Wavelength • tanh = hyperbolic tangent • h = water depth Held at the University of Washington in Seattle, Washington (USA) , During July 21- August 2, 2007.

  6. The Certificate Program in Tsunami Science and Preparedness. or m/s m/s or • Wave motion: Speed Approximations • For h > L/2 (L < 2h)  Deep-water waves • If x is larger than , then tanh x ~ 1 • tanh (2h/L) = 1 (within 0.5%) The wavelength is the only variable affecting the wave speed! Held at the University of Washington in Seattle, Washington (USA) , During July 21- August 2, 2007.

  7. The Certificate Program in Tsunami Science and Preparedness. • Wave motion: Speed Approximations • For h > L/2  Deep-water waves Circular motion of particles Exponential decrease of path with depth! Held at the University of Washington in Seattle, Washington (USA) , During July 21- August 2, 2007.

  8. The Certificate Program in Tsunami Science and Preparedness. or m/s • Wave motion: Speed Approximations • For h < L/20 (L > 20h)  Shallow-water waves • If x is small, then tanh x ~ x • tanh (2h/L) = (2h/L) (within 3%) Or: C= L/T = (gh)1/2  L = 3.13 (h)1/2.T The water depth is the only variable affecting the wave speed! Held at the University of Washington in Seattle, Washington (USA) , During July 21- August 2, 2007.

  9. The Certificate Program in Tsunami Science and Preparedness. • Wave motion: Speed Approximations • For h < L/20  Shallow-water waves Elliptical motion of particles Exponential decrease of vertical path with depth Not of horizontal path! Held at the University of Washington in Seattle, Washington (USA) , During July 21- August 2, 2007.

  10. The Certificate Program in Tsunami Science and Preparedness. A B Held at the University of Washington in Seattle, Washington (USA) , During July 21- August 2, 2007.

  11. The Certificate Program in Tsunami Science and Preparedness. Held at the University of Washington in Seattle, Washington (USA) , During July 21- August 2, 2007.

  12. The Certificate Program in Tsunami Science and Preparedness. Wave progression toward shore Held at the University of Washington in Seattle, Washington (USA) , During July 21- August 2, 2007.

  13. The Certificate Program in Tsunami Science and Preparedness. Held at the University of Washington in Seattle, Washington (USA) , During July 21- August 2, 2007.

  14. The Certificate Program in Tsunami Science and Preparedness. Wave Diffraction- Propagation of a wave around an obstacle Wave Reflection- a progressive wave striking a vertical barrier and being reflected in the direction from where they came Held at the University of Washington in Seattle, Washington (USA) , During July 21- August 2, 2007.

  15. The Certificate Program in Tsunami Science and Preparedness. Transformation of Shallow-water Waves • As waves enter shallow water • Wavelength shortens • Height increases • Speed decreases Held at the University of Washington in Seattle, Washington (USA) , During July 21- August 2, 2007.

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