Wave Transport and Wet Beaches
Country: United States
Date: February 6, 2005
My daughter, studying wave theory, read the following:
Waves are seen to move through an ocean or lake; yet the water always
returns to its rest position. Energy is transported through the medium,
yet the water molecules are not transported. Proof of this is the fact
that there is still water in the middle of the ocean. The water has not
moved from the middle of the ocean to the shore. If we were to observe a
gull or duck at rest on the water, it would merely bob up-and-down in a
somewhat circular fashion as the disturbance moves through the water; the
gull or duck always returning to its original position. The gull or duck
is not transported to the shore because the water on which it rests is not
transported to the shore. In a water wave, energy is transported without
the transport of water.
Her response: Baloney! if that is so, then why is the beach wet? (don't
you love how teenagers get right to the point?)
If the water in an ocean wave is only moving up and down, why do waves
travel onto the beach? (Is the above paragraph completely correct?)
Strange as it appears, a given "element" of water undergoes a roughly
circular motion moving up and down. This has been verified by suspending
particles with the same density as water and watching their motion.
Nonetheless the wave train moves forward, as tsunami disasters have
recently shown. An analogy is in fact the motion of an "old time" steam
locomotive in which the motion of the wheels connected by their connecting
bar is approximately "up and down" even though the locomotive as a unit
moves forward at a high rate of speed. Hmmm! Trying to find an "old time"
steam locomotive may be a challenge.
Give credit to your daughter for being both incisive and insightful.
On the one hand, the text is correct in stating that the water is simply a
medium for the energy that is travelling through it in the form of a wave
and in a simple, ideal system, no water is transported as the wave passes
On the other hand, wave dynamics - especially by shorelines is a very
complex. Let me try to hit on some of the pertinent details. In deep
water, energy can travel through the water without interacting with
anything, and so we see the "top" of the wave and it can be as simple as
the text described. As a wave approaches the shore however, since the
sandy bottom is at an incline, there will come a point that the amplitude
of the wave will be higher than the total depth of the water. And so the
wave will "drag" along the bottom - or more precisely, the energy will
interact with the sandy bottom and the energy will be refracted,
reflected, etc - causing the energy to go in a different direction other
than toward the shore. This will cause the water to rise. As the energy
that is more on the surface of the water pushes towards the shore, and the
energy that has hit the bottom push back away from the shore - "meet", the
water will form a curl, the wave "breaks". From this alone, one can
imagine why there is transport of water at the shore.
Throw in the idea that the wave may not be coming at a direct right angle
to the shore and you can see that the energy will produce even more
complex patterns. Add the idea that as the many different waves -from the
bottom, from the top, caused by natural barriers, and wind- interact then
shear forces can be created in the water - where one part of the water
will feel a force in one direction, while another feels a different
direction, and then actual currents actually do form.
So, what the text is really saying is that the water is not the wave -
energy is the wave and water is the medium for that wave. But, points for
your daughter for recognizing that the water-wave system is not as simple
as all that.
Greg (Roberto Gregorius)
In theory, with no friction, the paragraph is correct,
and for the most part in the real world it is correct.
However, because of frictional forces, the medium (water or air)
is carried a short distance by the wave motion. The
same effect as ocean waves can be seen in stratoform
clouds near an atmospheric layer boundary, forming
waves in the cloud tops that carry the cloud droplets
a short distance (sometimes these waves actually break,
just as in the ocean, carrying the water droplets vertically
as well as horizontally).
Furthermore, in a similar way, a gull sitting in the water
near shore will be slowly transported towards the beach (as
long as his feet are being affected by an undertow beneath
the surface). Obviously, that is how driftwood, shells, etc.
get to the beach.
David R. Cook
Atmospheric Physics and Chemistry Section
Environmental Research Division
Argonne National Laboratory
The paragraph below is correct, but there is one more part to the story that
may satisfy your daughter. The wave causes the water to move vertically...
that is true. Yet, we also know that gravity causes a fluid to seek its own
Try to "stack" water up on a table. It does not work because it will seek its
own level. When the water is raised up near the shore, its tendency to seek
its own level causes it to move out and cover the land. When the trough of
the wave reaches the shore, the water recedes again seeking its own level.
The water lapping up on the shore is not directly caused by the wave, but
rather by the action of the water to being raised by the wave's energy.
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