Transformation of Shallow-Water Waves The Certificate Program in Tsunami Science and Preparedness....
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Transcript of Transformation of Shallow-Water Waves The Certificate Program in Tsunami Science and Preparedness....
Transformation of Shallow-Water Waves
TThe Certificate Program in Tsunami Science and Preparednesshe Certificate Program in Tsunami Science and Preparedness..
HeldHeld at the University of Washington in Seattle, Washington (USA) at the University of Washington in Seattle, Washington (USA) , , DDuring July 21- August 2, 2007.uring July 21- August 2, 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.
TThe Certificate Program in Tsunami Science and Preparednesshe Certificate Program in Tsunami Science and Preparedness..
HeldHeld at the University of Washington in Seattle, Washington (USA) at the University of Washington in Seattle, Washington (USA) , , DDuring July 21- August 2, 2007.uring July 21- August 2, 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
TThe Certificate Program in Tsunami Science and Preparednesshe Certificate Program in Tsunami Science and Preparedness..
HeldHeld at the University of Washington in Seattle, Washington (USA) at the University of Washington in Seattle, Washington (USA) , , DDuring July 21- August 2, 2007.uring July 21- August 2, 2007.
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.
TThe Certificate Program in Tsunami Science and Preparednesshe Certificate Program in Tsunami Science and Preparedness..
HeldHeld at the University of Washington in Seattle, Washington (USA) at the University of Washington in Seattle, Washington (USA) , , DDuring July 21- August 2, 2007.uring July 21- August 2, 2007.
Wave motion: Speed and energyWave motion: Speed and energyThere are mathematical relationships linking the There are mathematical relationships linking the characteristics of wavelength (L), wave period (T) and characteristics of wavelength (L), wave period (T) and wave height (H) to wave speed and to wave energy.wave height (H) to wave speed and to wave energy.Wave speed Wave speed speed = distance/time speed = distance/timeC = L/T (time one wavelength takes to pass a certain C = L/T (time one wavelength takes to pass a certain point)point)Wave speed can also be represented by the equation:Wave speed can also be represented by the equation:
Where:Where:g = acceleration due to gravityg = acceleration due to gravityL = WavelengthL = Wavelengthtanh = hyperbolic tangenttanh = hyperbolic tangenth = water depthh = water depth
)2
tanh(2 L
hgL
T
LC
TThe Certificate Program in Tsunami Science and Preparednesshe Certificate Program in Tsunami Science and Preparedness..
HeldHeld at the University of Washington in Seattle, Washington (USA) at the University of Washington in Seattle, Washington (USA) , , DDuring July 21- August 2, 2007.uring July 21- August 2, 2007.
Wave motion: Wave motion: Speed Speed ApproximationsApproximations
1)1) For h > L/2 (L < 2h) For h > L/2 (L < 2h) Deep-water waves Deep-water waves
If x is larger than If x is larger than , then tanh , then tanh x ~ 1 x ~ 1
tanh (2tanh (2h/L) = 1 (within 0.5%)h/L) = 1 (within 0.5%)
)2
tanh(2 L
hgL
T
LC
The The wavelengthwavelength is the is the onlyonly variable affecting the wave speed! variable affecting the wave speed!
2
gL
T
LC or L25.1 m/s
π
gT
T
LC
2 T56.1or m/s
TThe Certificate Program in Tsunami Science and Preparednesshe Certificate Program in Tsunami Science and Preparedness..
HeldHeld at the University of Washington in Seattle, Washington (USA) at the University of Washington in Seattle, Washington (USA) , , DDuring July 21- August 2, 2007.uring July 21- August 2, 2007.
Wave motion: Speed Wave motion: Speed ApproximationsApproximations
1)1) For h > L/2 For h > L/2 Deep-water waves Deep-water waves
Circular motion of particlesCircular motion of particlesExponential decrease of path with depth!Exponential decrease of path with depth!
TThe Certificate Program in Tsunami Science and Preparednesshe Certificate Program in Tsunami Science and Preparedness..
HeldHeld at the University of Washington in Seattle, Washington (USA) at the University of Washington in Seattle, Washington (USA) , , DDuring July 21- August 2, 2007.uring July 21- August 2, 2007.
Wave motion: Speed Wave motion: Speed ApproximationsApproximations
2)2) For h < L/20 (L > 20h) For h < L/20 (L > 20h) Shallow-water Shallow-water waveswaves
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%))
2tanh(
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
TThe Certificate Program in Tsunami Science and Preparednesshe Certificate Program in Tsunami Science and Preparedness..
HeldHeld at the University of Washington in Seattle, Washington (USA) at the University of Washington in Seattle, Washington (USA) , , DDuring July 21- August 2, 2007.uring July 21- August 2, 2007.
Wave motion: Speed Wave motion: Speed ApproximationsApproximations
2)2) For h < L/20 For h < L/20 Shallow-water waves Shallow-water waves
Elliptical motion of Elliptical motion of particlesparticles
Exponential decrease of Exponential decrease of verticalvertical path with path with depthdepth
Not of horizontal path!Not of horizontal path!
TThe Certificate Program in Tsunami Science and Preparednesshe Certificate Program in Tsunami Science and Preparedness..
HeldHeld at the University of Washington in Seattle, Washington (USA) at the University of Washington in Seattle, Washington (USA) , , DDuring July 21- August 2, 2007.uring July 21- August 2, 2007.
A
B
TThe Certificate Program in Tsunami Science and Preparednesshe Certificate Program in Tsunami Science and Preparedness..
HeldHeld at the University of Washington in Seattle, Washington (USA) at the University of Washington in Seattle, Washington (USA) , , DDuring July 21- August 2, 2007.uring July 21- August 2, 2007.
TThe Certificate Program in Tsunami Science and Preparednesshe Certificate Program in Tsunami Science and Preparedness..
HeldHeld at the University of Washington in Seattle, Washington (USA) at the University of Washington in Seattle, Washington (USA) , , DDuring July 21- August 2, 2007.uring July 21- August 2, 2007.
Wave progression toward shore
TThe Certificate Program in Tsunami Science and Preparednesshe Certificate Program in Tsunami Science and Preparedness..
HeldHeld at the University of Washington in Seattle, Washington (USA) at the University of Washington in Seattle, Washington (USA) , , DDuring July 21- August 2, 2007.uring July 21- August 2, 2007.
TThe Certificate Program in Tsunami Science and Preparednesshe Certificate Program in Tsunami Science and Preparedness..
HeldHeld at the University of Washington in Seattle, Washington (USA) at the University of Washington in Seattle, Washington (USA) , , DDuring July 21- August 2, 2007.uring July 21- August 2, 2007.
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
TThe Certificate Program in Tsunami Science and Preparednesshe Certificate Program in Tsunami Science and Preparedness..
HeldHeld at the University of Washington in Seattle, Washington (USA) at the University of Washington in Seattle, Washington (USA) , , DDuring July 21- August 2, 2007.uring July 21- August 2, 2007.
Transformation of Shallow-water Waves
• As waves enter shallow water
– Wavelength shortens
– Height increases
– Speed decreases
TThe Certificate Program in Tsunami Science and Preparednesshe Certificate Program in Tsunami Science and Preparedness..
HeldHeld at the University of Washington in Seattle, Washington (USA) at the University of Washington in Seattle, Washington (USA) , , DDuring July 21- August 2, 2007.uring July 21- August 2, 2007.