Wave Hydrodynamics.
Beach Terminology
The inner shelf is a friction-dominated realm where surface and bottom boundary layers overlap. (From Nitrouer, C.A. and Wright, L.D., Rev. Geophys., 32, 85, 1994. With permission.)
Conceptual diagram illustrating physical transport processes on the inner shelf. (From Nitrouer, C.A. and Wright, L.D., Rev. Geophys., 32, 85, 1994. With permission.)
Ocean Waves Ocean waves may be classified by the generating force (wind, seismic events, or gravitational pull of the moon), the restoring force, (surface tension, gravity, the earth s rotation), or the frequency of the waves. Idealized Ocean Wave Spectrum
A wind wave is generated by the friction of the wind over the water s surface. Wind Waves As the wind blows over the surface of the water, friction and pressure differences create small ripples in the water surface. The wind pushes on the back side of the wave and pulls on the front, transferring energy and momentum to the water. As the wind continues to transfer momentum to the water, the wave becomes higher.
Wave Growth The area where wind waves are form and grow is called the generation area. The heights of the waves in the generation area are determined by three factors: wind speed, duration, and fetch. Higher wind speeds mean more momentum to transfer to the water, resulting in higher waves. Duration is the length of time the wind is blowing. The longer the wind blows, the higher the waves and more chaotic the seas.
Fetch Fetch is the horizontal distance that the wind blows across the water. Fetch is important in the early stages of wave formation, and will control how large the wave will be at a given time.
Swell As deep-water waves depart the generation area, they disperse with the long waves travel faster. This sorting by wave speed creates long regular wave patterns called swell.
Shoaling Waves As a wave shoals (approaches the shoreline) the wave period remains constant, causing the wavelength to decrease and the wave height to increase. Friction slows the bottom of the wave to while the top continues at the same speed, causing the wave to tip forward. When H/L, the ratio of the wave height to wavelength, reaches the critical value of 1/7, the wave breaks.
SEAS Waves under the influence of winds in a generating area SWELL Waves moved away from the generating area and no longer influenced by winds
SMALL AMPLITUDE/FIRST ORDER/AIRY WAVE THEORY 1. Fluid is homogenous and incompressible, therefore, the density is a constant. 2. Surface tension is neglected. 3. Coriolis effect is neglected. 4. Pressure at the free surface is uniform and constant. 5. Fluid is ideal (lacks viscosity).
SMALL AMPLITUDE/FIRST ORDER/AIRY WAVE THEORY 6. The wave does not interact with any other water motion. 7. The bed is a horizontal, fixed, impermeable boundary which implies that the vertical velocity at the bed is zero. 8. The wave amplitude is small and the wave form is invariant in time and space. 9. Waves are plane or low crested (two dimensional). Can accept 1, 2, and 3 and relax assumptions 4-9 for most practical solutions.
WAVE CHARACTERISTICS T = WAVE PERIOD Time taken for two successive crests to pass a given point in space
Definition of Terms ELEMENTARY, SINUSOIDAL, PROGRESSIVE WAVE h=eta
WAVE CELERITY, LENGTH, AND PERIOD PHASE VELOCITY/WAVE CELERITY: (C) speed at which a waveform moves. Relating wavelength and H 2 O depth to celerity, then Since C = L/T, then is NOTE: L exists on both sides of the equation.
Here, When d/l >0.5 = DEEP WATER Since: Then: Since: Then: DEEP WATER:
1. Longer waves travel faster than shorter waves. 2. Small increases in T are associated with large increases in L. Long waves (swell) move fast and lose little energy. Short wave moves slower and loses most energy before reaching a distant coast.
MOTION IN A SURFACE WAVE Local Fluid Velocities and Accelerations (HORIZONTAL) (VERTICAL)
Water particle displacements from mean position for shallow-water and deepwater waves.
As waves approach a shoreline the water shallows and they change from deepwater to transitional waves. As water shallows the waves steepen and finally break to form surf which surges towards the shoreline.
When surf reaches the beach it rushes up the beach face as swash and then runs back down the slope as backwash. Swash and backwash moves sediment up and down the beach face.
SUMMARY OF LINEAR WAVES C = Celerity = Length/Time Relating L (Wavelength) and D (Water Depth) Since C = L/T, then becomes: Since C = L/T, then becomes:
PROBLEMS GIVEN: A wave with a period T = 10 secs. is propagated shoreward from a depth d = 200m to a depth d = 3 m. FIND: C and L at d = 200m and d = 3m.
WAVE ENERGY AND POWER Kinetic + Potential = Total Energy of Wave System Kinetic: due to H 2 O particle velocity Potential: due to part of fluid mass being above trough. (i.e. wave crest)
WAVE ENERGY FLUX Rate at which energy is transmitted in the direction of progradation. (Wave Power)
Summary of LINEAR (AIRY) WAVE THEORY: WAVE CHARACTERISTICS
Regions of validity for various wave theories.
HIGHER ORDER THEORIES 1. Better agreement between theoretical and observed wave behavior. 2. Useful in calculating mass transport. HIGHER ORDER WAVES ARE: More peaked at the crest. Flatter at the trough. Distribution is skewed above SWL.
Comparison of second-order Stokes profile with linear profile.
USEFULNESS OF HIGHER ORDER THEORIES MASS TRANSPORT VELOCITY = U(2) The distance a particle is displaced during one wave period. NB: Mass transport in the direction of propagation.
Stokes HIGHER ORDER WAVES Takes wave height to 2 nd order (H 2) and higher Useful in higher energy environments 2 nd order approximate wave profile is:
For deep H2O Eq. reduces to: If H/L is small, then profile can be represented by linear wave theory TERM: Peaks crests Flattens troughs Conforms to shallow H 2 O wave profile THIRD ORDER APPROX. (Wave Velocity) NB. If (H/L) is small, use linear wave theory equation.
VELOCITY OF A WAVE GROUP WAVE GROUP/WAVE TRAIN Speed not equal to wave travel for individual waves GROUP SPEED = GROUP VELOCITY (Cg). INDIVIDUAL WAVE SPEED = Phase velocity or wave celerity. Waves in DEEP or TRANSITIONAL WATER In SHALLOW WATER
K =.4085376 YT = 1.065959 Keulegan and Patterson (1940) Cnoidal Wave Theory SI Units (m) Wave Height =.25 Wave Period = 2 WaterDepth = 1.1 Deep Water Length = 6.24 Present Length = 3.757897 Elliptical Modulus =.4085376 Net Onshore Displacement Umass = Mass Transport Velocity
Airy Wave Theory LO = 6.24 L = 5.783304 Time U(T) UMass Sediment Transport T = 2s H = 0.25m D = 1.5m NB. Umass Symmetry
Airy Wave Theory LO = 6.24 L = 5.363072 Time U(T) UMass Sediment Transport T = 2s H = 0.25m D = 1.1m Depth at which C.T. took place
Deformasi Gelombang Breaking Refraction Diffraction Reflection 44
Refraction Waves travel more slowly in shallow water (shallower than the wave base). This is called refraction This causes the wave front to bend so it is more parallel to shore. It focuses wave energy on headlands. 45
European Coast, 1996 Wave Refraction Orthogonal Surf / Breaker Zone Beach 46
Wave Refraction Seabed contour Wave Crest Path of crests diverge and minimize impact of waves on shore Wave crest Seabed contour Path of crests converge and maximize impact of waves on shore Shallow Deep 47
Long shore Transport 48
Wave Diffraction 49
Wave Diffraction Hd q Hi r b L Breakwater Shadow Zone Wave Diffraction Orthogonal Energy Transfer Wave Crest Orthogonal Diffraction Coeficient ( K ) K = Hd / Hi K = f (r/l, 50 b, q)
European Coast, 1996 Refleksi Gelombang 51
Refleksi Gelombang Untuk dinding vertikal, kedap air, dgn elevasi diatas muka air, hampir seluruh energi akan dipantulkan kembali ke laut. Hanya sebagian saja energi yang dipantulkan jika gelombang menjalar di pantai yang agak landai Refleksi tergantung pada kelandaian pantai, kekasaran dasar laut, porositas dinding, dan Angka Irribarren (Ir) : Kr = Hr / Hi Kr = fungsi (a, n, P, Ir) I r tan H L i o 52
Perbedaan Gelombang 53
WAVES BREAKING 0.5 tan b H o L o 0.5 3.3 3.3 Dean and Dalrymple, 2002
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