Representing
Breaking Waves In Computer Graphics / Daniel Blacker / 07/03/05
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1.
Abstract 2.Introduction
3.Ocean Waves 4.Waves
in CG 5.Tool Development
6. Conclusion 7.
References 8. Code
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3.1
Overview In
order to accurately simulate breaking ocean waves in 3d, we must
first look at the principles behind the propagation and dynamics
of water waves.
When developing
our tool we can study the swell that breaks on Bournemouth sea-front
as a real life example. The principles surrounding these waves are
the same that affect any breaking ocean wave regardless of scale,
even those of the 20ft waves that break off the reefs of Hawaii.
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Fig.2 - Waves
Breaking on Bournemouth Sea Front |
Looking
at Figure.2 the first sign of the approaching wave we see
is the long line of shadow visible sweeping towards the shore, forming
an obvious ridge of water gaining height as it advances. As it approaches
the beach a white foaming top is formed and curling breakers are
created.
The water we
see as the wave is forming is not the same water we observe breaking
at the shore. The `Grandfather's axe' analogy can be applied to
ocean waves:
’A
man is very proud of an axe that once belonged to his grandfather,
and he says it has only needed three new handles and two new heads
since his grandfather’s time. The axe he owns is made from
material that his grandfather never saw, what right has he to claim
it is his grandfather's axe?’ [2]
We witness something
travelling across the sea to the shore. If it isn't the water then
what is it? You could call it a shape, a pattern of outline and
water motion. The water, however, is a more permanent and real thing
than the wave and cannot disappear. The wave, which is merely a
pattern, can grow or shrink or fade out altogether.
`It must
be emphasised that a travelling wave is a passage of motion only,
not of water. The actual movement of the water particles that compose
the wave is relatively very small' [3]
`Ocean waves,
like all other waves, are defined as travelling disturbances that
carry energy from place to place.' [4] |
3.2
Wave Propagation
Waves are created
by a combination of wind and gravity. The ocean would be a flat
pool of water without any waves. The creation of waves begins in
a storm area. As the winds blow, the surface of the water is pushed
away from the storm area and swell is generated. The sizes of the
waves decrease as they leave the storm area. The size and shape
of the waves when they eventually reach the shore depends on the
`fetch', which is the extent of open water between the observer
and the source. |

Fig.2
- Storm Source of a Wave [2]
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The
hydrodynamics of ocean waves is highly non-linear, and can become
very complex. Here we will outline some of the underlying principles
that affect the progression of a breaking wave. |
After
the waves are created, they must usually travel across deep ocean
areas. Here the water `particles' rotate in a circle, forward at the
crest and backward at the trough. This means there is no net motion
of the particles as the wave passes through them. For these deep ocean
waves the circular motion diminishes exponentially with depth, becoming
negligible at depths greater than the wavelength of the wave (distance
between two successive peaks). |
Fig.4 - Motion
of Water Particles[11] |
Fig.5 - Wave
Motion Derived from Orbital Flow[11] |
3.3 Breaking Waves
As a wave approaches
the shore, the depth at the crest is larger than at the trough,
where shallow water wave theory shows the speed is lower, so the
crest overtakes the trough, the peak sharpens and the wave eventually
breaks. Waves breaking on sloping beaches may be of two kinds: plunging
and spilling:
`Waves break
and form `whitecaps' when: the angle between front and back side
of the wave <120°, and its height is 1/7th of its wavelength'[5]
`Spilling
breakers are concave on both faces, so that the wave profile resembles
a cycloid. The wave ravels away at its unstable, thin crest as it
advances' [6]
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Small
swell conditions and offshore winds lead to these spilling breakers.
Such a wave gradually loses its form as water spills from its crest.
`The plunging
breaker has a well rounded back and a concave front. In fact just
as the crest plunges forward into the trough, a swimmer dead to
prudence can look upward through a solid overhang of water' [6]
When a plunging
wave reaches the shore, factors such as the shape of the beach and
wind conditions affect how the wave breaks. The wave could plunge
all at once or could break at various points forming numerous crests
along its length.
The difference
in the two types of waves as regards to accurately simulating them
in 3d is substantial as we will go on to discuss.
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Fig.6 - Plunging
and Spilling Waves [6] |
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Page
3 - Ocean Waves |
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