1. Juan Carlos Ortiz Royero Ph.D.
Wave Hydrodynamics
Juan 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

2. 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

3. 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, With permission.)

4. Conceptual diagram illustrating physical transport processes on the inner shelf.
(From Nitrouer, C.A. and Wright, L.D., Rev. Geophys., 32, 85, With permission.)

5. Approximate distribution of ocean surface wave energy illustrating the classification of surface waves by wave band, primary disturbance force, and primary restoring force.

6. 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

7. Time taken for two successive crests to pass a given point in space
WAVE CHARACTERISTICS
T = WAVE PERIOD
Time taken for two successive crests to pass a given point in space

8. Wave Pattern Combining Four Regular Waves

9. 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)

10. Regular Waves

11. Governing equations Conservation of Mass: Continuity equation,
for incompressible fluids
Velocity potential

12. Navier- Stokes equation
Governing equations
Laplace Equation:
Navier- Stokes equation
p is pressure
is the water density
 is diffusion coefficient

13. Unsteady Bernoulli equation:
Fluid is incompressible, no viscous, irrotational, etc..
Euler equation:
Unsteady Bernoulli equation:

14. 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

15. Solution (Airy 1845, Stokes 1847) :
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) :

16. Dispersion relationship

17. Deep water
Intermediate water
Shallow water

19. 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.

20. 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.

21. Velocity components of the fluid particles
(HORIZONTAL)
(VERTICAL)

22. Motions of the fluid particles

23. Kinetic + Potential = Total Energy of Wave System
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)

24. WAVE ENERGY FLUX (Wave Power)
Rate at which energy is transmitted in the direction of progradation.

25. HIGHER ORDER THEORIES HIGHER ORDER WAVES ARE:
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.

26. Comparison of second-order Stokes’ profile with linear profile.

27. Stokes, 1847

28. Waves theories

29. Regions of validity for various wave theories.

30. Conclusions Linear Wave Theory: Simple, good approximation for
70-80 % engineering applications.
Nonlinear Wave Theory: Complicated, necessary for about % engineering applications.
Both results are based on the assumption of non-viscous flow.

31. Thanks!!