Transformation of Shallow-Water Waves Annual National Symposium on Computational Science and...

Transformation of Shallow-Water Waves

Annual National Symposium on Computational Science and Engineering (ANSCSE11) Annual National Symposium on Computational Science and Engineering (ANSCSE11) Held at Phuket, Thailand, March 28-30, 2007Held at Phuket, Thailand, March 28-30, 2007


Joint Regional Conference on Disaster Relief and Management – International Cooperation & Role of ICTJoint Regional Conference on Disaster Relief and Management – International Cooperation & Role of ICTHeldHeld atat Alexandria, Alexandria, Egypt Egypt during the period from 14 to 17 April 2007during the period from 14 to 17 April 2007


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.




Joint Regional Conference on Disaster Relief and Management – International Cooperation & Role of ICTJoint Regional Conference on Disaster Relief and Management – International Cooperation & Role of ICTHelpHelp atat Alexandria, Alexandria, Egypt Egypt during the period from 14 to 17 April 2007during the period from 14 to 17 April 2007


Annual National Symposium on Computational Science and Engineering (ANSCSE11) Annual National Symposium on Computational Science and Engineering (ANSCSE11)

Held at Phuket, Thailand, March 28-30, 2007Held at Phuket, Thailand, March 28-30, 2007






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.






Wave motion: Speed Wave motion: Speed ApproximationsApproximations

For h < L/20 (L > 20h) For h < L/20 (L > 20h) Shallow-water waves Shallow-water waves

If x is small, then tanh x ~ x If x is small, then tanh x ~ x

tanh (2tanh (2h/L) = (2h/L) = (2h/L) (within 3%)h/L) (within 3%))2

tanh(2 L

hgL

T

LC

Or: C= L/T = (gh)Or: C= L/T = (gh)1/2 1/2 L = 3.13 (h) L = 3.13 (h)1/21/2.T.TThe water depth is the only variable affecting the wave speed!The water depth is the only variable affecting the wave speed!

or h1.3ghT

LC m/s










A

B


Wave progression toward shore






• Bending of the wave crest as waves enter shallow water. It is due to– Drag along the

bottom.– Differential

speed along the crest.

Wave Wave RefractiRefractionon






Wave Diffraction- Propagation of a wave around an obstacleWave Reflection- a progressive wave striking a vertical barrier and being reflected in the direction from where they came






Transformation of Shallow-water Waves

• As waves enter shallow water

– Wavelength shortens

– Height increases

– Speed decreases






Jamboree – II, The JCOMM/IODE Combined Modeling and Data Management Training Workshop Jamboree – II, The JCOMM/IODE Combined Modeling and Data Management Training Workshop Held at Oostende, Belgium, 9 – 14 October 2006Held at Oostende, Belgium, 9 – 14 October 2006




Transformation of Shallow-Water Waves Annual National Symposium on Computational Science and...

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