wave hydrodynamics juan carlos ortiz royero ph.d. from:...
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Wave HydrodynamicsJuan Carlos Ortiz Royero Ph.D.
From:
wavcis.csi.lsu.edu/ocs4024/ocs402403waveHydrodynamics.ppt and the book: wind generated ocean wave by Ian R. Young 1999
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Fields Related to Ocean Wave
•Ocean Engineering: Ship, water borne transport, offshore structures (fixed and floating platforms). • Navy: Military activity, amphibious operation,
• Coastal Engineering: Harbor and ports, coastal structures, beach erosion, sediment transport
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The inner shelf is a friction-dominated zone where surface and bottom boundary layers overlap. (From Nitrouer, C.A. and Wright, L.D., Rev. Geophys., 32, 85, 1994. With permission.)
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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.)
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Approximate distribution of ocean surface wave energy illustrating the classification of surface waves by wave band, primary disturbance force, and primary restoring force.
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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
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WAVE CHARACTERISTICS
T = WAVE PERIOD
Time taken for two successive crests to pass a given point in space
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Wave Pattern Combining Four Regular Waves
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Linear Wave or small amplitude theory
• Assumptions:– The water is of constant depth d– The wave motion is two-dimensional– The waves are of constant form (do not
change with time)– The water is incompressible– Effect of viscocity, turbulence and surface
tension are neglected.– The wave height H: H / L 1 and H /d 1 ( L
is the wave length)
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Regular Waves
1; -- frequency (1/s) and -- Wave period
/ 2 a -- amplitude and -- Wave height
f f TT
a H H
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Governing equations
• Conservation of Mass:
ztzxw
xtzxu
),,(
),,( Velocity potential
01
udt
d
Continuity equation, for incompressible fluids
0
z
w
y
v
x
u
0 u
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Governing equations
• Laplace Equation:
• Navier- Stokes equation
02
2
2
2
zx
uFpdt
ud 21
p is pressureis the water density is diffusion coefficient
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0
gzp
t
• Euler equation:
• Unsteady Bernoulli equation:
Fluid is incompressible, no viscous, irrotational, etc..
Fpdt
ud
1
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Boundary conditions
• Dynamic boundary condition at the free surface:
In z = , p = 0
• Kinematic boundary condition at the free surface:
In z = , there can be no transport of fluid through the
free surface (the vertical velocity must equal the vertical
of the free surface
0
gt
xu
tdt
dw
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Boundary conditions
• Kinematic boundary condition at the bed:
In z = - d, there can be no transport of fluid through the
free surface (the vertical velocity must equal zero)
Solution (Airy 1845, Stokes 1847) :
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)sin(),,( wtkxatzx
)tanh(2 kdgk Dispersion relationship
kC
)tanh(kdk
gC
)sin(
)cosh(
)(cosh
2wtkx
kd
zdkgH
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Deep water
k
gC
Intermediate water
)tanh(kdk
gC
gdC
Shallow water
Lg
C2
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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.
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Example: What is the fase velocity of tsunami in deep water?
Solution: The typical wave length of a tsunami is thousand of kilometers and periods of hours. Since the wave length of tsunami is very large compared with the depth, then tsunami is a shallow water wave.
hkmgdC /800
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Velocity components of the fluid particles
(VERTICAL)
(HORIZONTAL)
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WAVE ENERGY AND POWER
Kinetic + Potential = Total Energy of Wave System
Kinetic: due to H2O particle velocity
Potential: due to part of fluid mass being above trough. (i.e. wave crest)
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WAVE ENERGY FLUX(Wave Power)
•Rate at which energy is transmitted in the direction of progradation.
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HIGHER ORDER THEORIES1. 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.
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Comparison of second-order Stokes’ profile with linear profile.
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Stokes, 1847
)(2cos)2cosh(2()(sinh
cosh
16
)sin(),,(
3
2
tkxkdkd
kdkH
wtkxL
Htzx
)(2sin
)(sinh
)(2cosh
32
3
)sin()cosh(
)(cosh
2
4
2
wtkxkd
zdkH
wtkxkd
zdkgH
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Waves theories
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Regions of validity for various wave theories.
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Conclusions
•Linear Wave Theory: Simple, good approximation for70-80 % engineering applications.
•Nonlinear Wave Theory: Complicated, necessary for about 20-30 % engineering applications.
•Both results are based on the assumption of non-viscous flow.
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Thanks!!