Wave Hydrodynamics

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Wave Hydrodynamics Juan Carlos Ortiz Royero
Ph.D. From wavcis.csi.lsu.edu/ocs4024/ocs402403
waveHydrodynamics.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
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Governing equations

• Conservation of Mass

Continuity equation, for incompressible fluids
Velocity potential
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Governing equations

• Laplace Equation
• Navier- Stokes equation

• p is pressure
• is the water density
• ? is diffusion coefficient

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Fluid is incompressible, no viscous,
irrotational, etc..

• Euler equation
• Unsteady Bernoulli equation

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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

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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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Dispersion relationship
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Deep water
Intermediate water
Shallow water
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• Longer waves travel faster than shorter waves.
• 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.
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Velocity components of the fluid particles

(HORIZONTAL)
(VERTICAL)
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Motions of the fluid particles
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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 THEORIES

• Better agreement between theoretical and observed
  wave behavior.
• 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
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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
  for
• 70-80 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!!