Motion of ship on waves.

1. Waves and Tides

2. Waves
 A disturbance which
moves through or over
the surface of a fluid
 Mostly caused by:
- Winds
- Earthquakes
- Gravitational Pull
- Volcanos

3.  Waves are created on the surface of water as the result
of a generating force.
 An additional force, called the restoring force, acts to
return the surface of the water to its original flat level.

4.  A generating force will create waves on the surface of
the water that will then move away from their point of
origin.
 The most common generating force is the blowing
wind.
 Other generating forces include vessels moving in or
on the water, landslides into water, submarine volcanic
eruptions, and submarine earthquakes.
 There are two different restoring forces that act on
water waves.
 surface tension and gravity.

5.  When a wave passes through the ocean, individual
water molecules move up and down but they do not
move forward or backward.

6. Water Motion in Waves
 Water travels in vertical
circular orbits
 Wave moves, particles don’t!

8. Importance of Waves
 Shaping Coastlines
 Erode cliffs
 Grind rock into sand
 Ecology
 Returns O2 to water
 Stir up food for filter
feeders

9. Wave Characteristics
 Parts of a Wave
 Crest = high point
 Trough = low point
 Height = vertical
distance from crest to
trough
 Wavelength =
Horizontal distance
between crest to crest or
trough to trough

10.  The resting or undisturbed sea surface is called the
equilibrium surface.
 The highest point on the wave is called the crest.
 The lowest point of the wave is called the trough.
 The distance between two successive crests or troughs
is called the wavelength.

11.  The vertical distance between the crest and the trough is the
wave height.
 The vertical distance between either the crest or the trough
of the wave and the equilibrium surface is the wave
amplitude. This is half of the wave height.

13.  The amount of time necessary for one wavelength to
pass by a stationary point is called the period of the
wave.
 Period is usually measured in seconds/cycle (cycle is
another term that can be used for wavelength in this
case).
 The number of wavelengths that pass a stationary point
in a unit amount of time is the wave frequency.
 Frequency is usually measured in cycles/second, the
reciprocal of the wave period.

14.  Most water waves begin as wind (the generating force)
blows over the water and friction causes wrinkles to
form on the surface.
 These are called ripples or capillary waves and their
restoring force is surface tension.
 Small areas of capillary waves can appear and
disappear rapidly giving the impression that they are
jumping from point to point over the surface.
 These rapidly moving patches have been called cat’s-
paws.

15.  As more energy is transferred to the water, the waves
will grow in size.
 This will increase the roughness of the surface and
make it even easier for the wind to transfer energy to
the water so the waves will grow in size rapidly.
 As the waves grow, gravity will become the restoring
force and the waves will be called gravity waves.

16.  The waves transports energy.
 There is relatively little transport of water in the
direction of wave propagation.
 The forward velocity of the water particles at the top of
their orbit is slightly greater than their backward
velocity at the bottom of their orbit. Hence, there is a
small net transport of water in the direction of wave
propagation.

17.  As a wave approaches, a water particle at the surface
will trace a circular path rising with the approaching
crest of the wave and falling with the passing trough.
The diameter of the circular orbit at the surface will
equal the height of the wave.
 The diameter of the orbital motion will decrease with
increasing depth until there is no motion at a depth of
approximately one-half of the wavelength.

21. 21
Wave Speed
 The speed of a wave, its wavelength, and its period
are all related to one another
 Wave speed is usually represented with the symbol C
which stands for celerity which is derived from a
Latin word meaning swift.
 The speed of a wave (C ) is equal to its wavelength (L
) divided by its period (T ).
C = ( L / T )

22. 22
Deep Water Waves
 Waves that propagate in water that is deeper than
one-half their wavelength are called deep-water
waves.
The orbital motion in the water column created by
deep-water waves stops before it reaches the sea floor.
 These waves cannot “feel” the bottom.
 The length and speed of a deep-water wave are
determined by its period.

23. 23
Deep-water waves
 In deep water, the wavelength of a wave is equal to
the acceleration of gravity [9.81 m/s2] (g ) divided by
two pi (2 π) times the period of the wave squared (T
2).
L = ( g / 2 π ) T 2
or
L = ( 1.56 m/s2 ) T 2

24. 24
Deep-water waves
( L / T ) = ( 1.56 m/s2 ) T

or, remembering that C = ( L / T )

C = 1.56 T
where C is measured in m/s and T is measured in
seconds.
C2= 1.56L
C= 1.25 sq. root L

25. 25
Progressive Wind Waves
(PWW)
 Waves that are actively growing because of the direct
influence of the wind are called forced waves. When these
waves move outward away from the direct influence of the
wind and they no longer continue to grow in size, they
become free waves.
 Once waves move away from the sea and become free waves
their period does not change as they continue to travel
through the oceans. The period of the wave will remain a
constant until the wave itself is altered or destroyed by
interaction with the bottom in shallow water or by breaking
on the shoreline.

26. 26
Dispersion: Longer period waves travel faster than shorter waves

27. 27
Swell approaching the coast

28. 28
Progressive Wind Waves (PWW)
 Multiple storms in the ocean basins may each generate
swell that propagates away from the storm centers.
These wave trains can intersect, and if they do, their
waveforms will add to each other when they meet and
then they will pass on out of the region where they
have met and continue once more as individual wave
trains.
 Waves can add constructively to produce waveforms
with greater height or they may add destructively and
cancel each other out.

29. 29

30. 30

31. 31
Wave Height
 The three most important factors controlling wave height are:
 the speed of the wind,
 how long the wind blows, and
 the size of the fetch, or the area the wind blows over in one direction.
 The maximum possible wave height increases as these three
factors increase.
 If any one of these factors is small, the wave height will be
small.

32. 32
Figure 9.12

33. 33

34. 34
Figure 9.20a

35. 35
Figure 9.20b

36. Trochoidal waves
 By observation the crests of ocean waves are sharper
than the troughs.
 The section of wave is generated by a fixed point
within a circle when that circle rolls along and under a
straight line.
 The crest of the wave occurs when the point is closest
to the straight line.
 The wavelength is equal to the distance the centre of
circle moves in making one complete rotation, i.e.
λ = 2π R

37.  The wave height is 2r = Hw
 X = RӨ – r sinӨ
 Z = r cosӨ

38. Sinusoidal waves
 Taking the x-axis in the still water surface, the same as
the mid-height of the wave and z-axis vertically down,
the wave surface height at x and time t can be written
as:
Z = (Hw/2) sin(qx+ωt)
 In this equation q = 2π/λ is termed as the wave no. and
ω = 2π/T is known as the wave frequency.
 T is the wave period.

41. Irregular waves
 The irregular wave surface is taken as the compound of
a large no. of small waves, each component wave
having its own length, height and direction.
 The wave heights could be taken as vertical distances
between successive crests and troughs, and the
wavelength measured between successive crests.

43.  If the wave heights measured are arranged in order of
reducing magnitude, the mean height of the highest
one-third of the waves is called the significant wave
height.

45. Wave spectra
 A ship’s motions in irregular ocean waves can be
synthesized from its motions in regular waves using
the energy spectrum concept.
 The components of the sea can be found by Fourier
analysis and the elevation of the sea surface at any
point and time can be represented by:
h =
 Where hn, ωn, & are the height, circular frequency
and orbitrary phase angle of the nth wave component.

46.  Within a small interval, dω, the energy in the waves can
be represented by half the square of the mean surface
elevation in that interval.
 Plotting this energy against ω gives what is termed as
Energy spectrum.
 The ordinate of the spectrum is usually denoted by S(ω).
 Since the ordinate represents the energy in an interval
whose units are 1/s its units will be (meter)2-seconds.
 S(ω) is called the spectral density.