INTRODUCTORY
OCEANOGRAPHYINTRODUCTORY
OCEANOGRAPHY
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In the third part of the lesson on ocean waves, we will explore the processes by which waves break when they shoal.
We learned in Part 1 that the celerity of a shallow water wave is directly proportional to water depth (d); therefore as a train of waves shoal (move into progressively more shallow water) they will slow down. The leading wave, being in the shallowest water, will slow before the wave just behind it, which will slow before the wave behind it, etc. Therefore, as the waves in the train shoal they will begin to "crowd up", with the second wave closing on the first wave, etc., and the wavelengths (L) between successive crests will decrease.
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Wave Shoaling and Breaking - the analogy of runners at the finish line |
Let
me return to the marathon analogy to illustrate this point. When the
runners cross the finish line they stop or begin walking very slowly.
Suppose a group of 10-15 runners were strung out in a line and, for
our illustration, evenly spaced 10 m apart. The first of the group to
cross the finish line would slow, but the second runner would be
running at full speed, so would close on the first. This crowding
process would continue as each one of the other 13 runner in turn
crossed the finish line.
This crowding of waves [and subsequent decrease in wavelength (L)] alone, can increase the steepness (H/L) of the leading waves, but the steepness also is increased because, as waves shoal, the wave height (H) increases (for reasons we will discuss in the next paragraph). This progressive increase of wave steepness is shown in Fig. 10.18 above, where the deepest portion of the leading wave slows more than the top portion, and the wave eventually becomes too steep and breaks, creating "surf".
I'd like to go into a bit more depth than the book to explain why H increases for shoaling waves. According to linear wave theory, the total amount of energy in a wave (TE) is equally partitioned between kinetic energy (KE) and potential energy (PE) in deep water. KE is the energy of motion, and in an ocean wave it is directly proportional to wave celerity, c. PE is the energy of position (think of lifting a ball and holding it above a bench -- its height above the bench is proportional to its PE and equal to the work required to lift the ball to that height) and is directly proportional to wave height, H. Therefore:
Waves slow when they shoal, and because KE a c, KE will decrease. Since TE is conserved (held constant), the decrease in KE is reflected in a comparable increase in PE, so wave height (H) is increased.
A simple example that shows this partitioning of energy should be instructive. Substitute numerical values for the energies in the equation above, and assume that TE is equal to 100 units and that KE and PE each have 50 units (wave theory partitions energy this way in deep water); i.e.,
So as waves shoal and KE decreases (say by 25 units) the energy transformation would result in
where total energy is conserved as PE increases by 25 units. Now, this increase in PE will result in an increase of H, H/L will increase doubly (remember H/L also is being increased because L decreases), and when the breaking criteria (H/L>1/7) is exceeded, the wave will break.
If you have tried to surf you know how quickly this transformation takes place. You must be in the proper position to catch the wave just before it breaks and as the water particles change from their orbital paths to a more horizontally-oriented translational path that hurls the water toward the beach. Is it any wonder that the force of breaking ocean waves can destroy just about any structure? If you doubt the force of a wall of water moving toward a structure, just remember how it felt the first time you did a "belly flop" off a low board into a swimming pool. Water is a fluid, but it also is dense enough to cause considerable damage when its full force is applied, particularly to flat, solid surfaces.
Up to this point, we have been discussing only waves generated on the water surface, the interface between water and air. It is also possible, however, for orbital progressive waves to be generated and propagate along density interfaces under the surface of the ocean. A strong pycnocline is such an interface (Fig. 10.25). The difference between the densities on either side of the pycnocline is not very large, certainly not as large as at the interface between water and air. Therefore, these internal waves will not propagate with nearly as much energy, even though their heights are above 100 m. They also propagate at much lower speeds than surface waves, but with longer periods (5 - 8 min.) and wavelengths (0.6 - 0.9 km). Parallel bands of slicks that are seen to move across the sea surface are attributed to internal waves, where converging water at the surface that follows behind the crest of the internal wave, dampens the surface waves.
Internal waves may be generated by undersea earthquakes or turbidity currents, or on a small scale by the movement of ships.
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