INTRODUCTORY
OCEANOGRAPHYINTRODUCTORY
OCEANOGRAPHY
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In the final part of this lesson we will discuss the standing waves that are set-up in lakes and which may be enhanced to produce resonance waves.
When two progressive waves of the same period move in opposite directions (usually after one of the waves is reflected off a solid surface with a zero angle of incidence), their product will result in a standing wave (SW) - see Fig. 10.24. A SW has a very special interference pattern because no net momentum is being carried by the SW (i.e., they are created by progressive waves with same periods moving in opposite directions, each carrying the same amount of momentum), and while the water particles still move vertically and horizontally (or with a combination of those directions), they do not move orbitally. SW's also oscillate, but not in the same way as in a progressive wave: there is the Node (or Nodal Line for a narrow-width basin) where all the particle motion is horizontal (no vertical movement of surface); and the Antinode (or Antinodal Line for a narrow-width basin) where the surface, and all the particle motion under the surface, is vertical. Between these two extremes, the particle motion is a combination of both movements.
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Nodes and Antinodes |
A crude visualization of the oscillation of the surface of a SW is to liken it to the way a "teeter-totter" (in the South some call it a "see-saw") moves, where the node is the connected pivot point and the seats are the antinodes. You also can observe a SW by setting a narrow, deep rectangular container half full of water on a table, then raising one end and dropping it slowly to the table top -- the SW will oscillate back and forth in a manner similar to that described above.
SWs set up in narrow enclosed rectangular basins are of three basic types, which I name and define a little more tightly than the book does. In the simplest SW, there is only one nodal line (think of the nodal line as the pivot-hinge that holds the see-saw to its base).
In the largest and longest east-west oriented lakes, the TPFs described earlier may cause very small-amplitude, forced SWs with semi-diurnal periods. Except in the unusual circumstance described below, these forced SWs are insignificant (with a range usually measured only in inches).
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Wind setup of Standing Waves |
A
strong wind blowing for a long period of time in a constant direction
along the long axis of a narrow enclosed basin (such as a continental
lake) will push the water to one end. This
"wind set-up" is not large, but
when the wind stops or "relaxes", the water at the high end of the
lake will run in the opposite direction and, after reflecting off the
other end, may create a small amplitude free SW. The SWs thus
generated will have periods determined by both the length and depth
of the basin:
where Lb is the length of the basin in meters, g is the acceleration of gravity (9.8 m/s2), h is the depth of the basin, and Tc is the characteristic period of the SW -- i.e., every time this basin is "excited" by the wind and a SW is produced, it will oscillate with the same period, very much as different length pipes on a closed-pipe organ have different characteristic frequencies (or periods) would. Therefore, these free SWs are "tuned" to their basin and, using the name given to such waves by the Swiss, are called seiche, as shown in Fig. 11.28 for Lake Geneva above.
I will not require you to calculate Tc using the full equation listed above, but only to remember the proportional relationship:
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Characteristic Periods of Basins |
Resonance SWs are a special combination of free and forced SWs. If a seiche has been set up by the wind with a Tc very nearly that of the period of the forced SW (TPF) and, most importantly, if Tc and the period of the TPF are in phase, then a small amplitude resonance tide may be set up in a basin. In other words, the resonance tide is a seiche that is "boosted" at just the right moment by the TPF to enhance its motion and, as a result, cause it to last longer and/or be larger than a totally free SW not so enhanced. The resonance tide set up in Lake Ontario is a good example of a free/forced SW.
You can compare this resonance tide to a child swinging in a swing. To start a child swinging requires the application of a fair amount of force to pull the seat back. When the seat is released, the child will begin swinging and the seat will oscillate with a Tc that is proportional to the length of the ropes of the swing. Left alone, the swing would soon stop, but if you time a very small extra "push" in phase with the characteristic period of the swing, it will continue (resonant) for as long as you like.
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