Oceanography
Unit 3
WAVES
Worksheet
Name
Period
The Motion of Water in Waves: We know from watching objects floating downstream
in rivers that floating objects move along with the water in which they float. It is
convenient to think of any body of water as being made up of parcels of water, or
masses of water. We can think of a floating object (say, a log) in the river as being
pushed along by the parcels of water surrounding it as they move downstream.
Now think of the appearance of waves traveling across the surface of the water
in a lake or ocean. If the water is relatively deep and we watch a log floating on the
surface we may see something different than we saw when we watched the log floating
downstream in the river. The waves may appear to travel across the water surface, but
the log does not travel along with them. At first glance it appears to bob up and down
upon the waves. If we look more carefully we see that, with each passing wave, the log
oscillates back and forth a bit in addition to moving up and down. (Still closer
observation indicates that it creeps forward, i.e. in the direction of wave travel, a very
little bit with each passing wave, but we will ignore that forward creep in this exercise.)
The primary motion of our log, or any other floating object, as the waves pass, is
circular motion in a vertical plane. As indicated above, similar circular motions of the
parcels of water surrounding the log create the circular motion. This motion is referred
to as orbital motion.
It is important to remember that the evidence we see when we watch the floating
log tells us that the motion of the water itself is very different from the motion of the
waves. The orbital motion of a parcel of water at the lake or sea surface as waves pass
is shown in Figure 1. Note that a parcel of water at the surface always stays essentially
at the surface as the wave passes.
Figure 1. Cross-section of a wave illustrating the orbital motion of parcels of water at the surface of a wave that is progressing from
left to right. The shape of the surface at one particular instant is shown by the heavy curve. Each circle depicts the motion of a
parcel of water at the surface of the ocean during the passage of a single wave. The base of each arrow indicates the location in
the orbit for selected parcels of water when the wave is in the position shown. The direction of each arrow indicates the direction in
which that parcel is moving when the wave is sin the position shown. For example, the left-most parcel of water is moving straight
upward.
Describe the orbital motion you would feel if you were floating in the waves out beyond
the breaker zone at the beach. Specifically, what motion would you feel at the very
crest of the wave?
Unit 3 – Waves and Currents
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Oceanography
What motion would you feel in the bottom of the trough?
Describe the motion you would feel as the wave advanced and carried you from the
trough to the crest?
As we look at the motions of parcels of water beneath the surface, we find that
the deeper we go the smaller the diameter of the orbit becomes. This is shown in
Figure 2.
Note that the individual parcels of water do not mix with one another. That is,
underneath any given point at the surface, all the parcels of water move up, down, or
sideways more or less together. The orbits get progressively smaller with increasing
depth. As a rough rule of thumb, we can say that the orbital diameter decreases by
approximately one half every time we increase the depth by (1/9) x L, where L is the
wavelength.
If the water depth is great enough so that the orbital motion at the bottom of the
lake or ocean is very small, the wave passes over the bottom without a great deal of
interaction with it. The wave does not “feel” the bottom. Such a wave is called a deepwater wave. When the bottom is sufficiently shallow so that there is significant
interaction between the bottom and the orbital motion of the water, the resulting waves
are called shallow-water waves.
Depth
Figure 2: Cross-section of a wave progressing from left to right, showing the decrease in orbital motion with increasing depth.
Circles at the left show orbits of several parcels of water under the crest of a wave. Each parcel is indicated by a small square. The
arrows show the direction of motion of those parcels. The circles at the right show orbits of several parcels of water under the
trough of a wave.
Unit 3 – Waves and Currents
2
Oceanography
Imagine a wave with a wavelength of 450 cm (approximately 13 feet). The orbital
diameter at the surface is essentially equal to the wave height (H), or, let us arbitrarily
say in this example, 64 cm (approximately 2 feet). Calculate the orbital diameter at the
depths indicated in the table below.
Depth (cm)
Orbital diameter (cm)
0
64
50
150
250
350
400
It is sometimes stated that orbital motion dies out at water depths deeper than one-half
the wavelength. Do you still think that is true?
Explain:
Unit 3 – Waves and Currents
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