INTRODUCTORY
OCEANOGRAPHYINTRODUCTORY
OCEANOGRAPHY
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In the second part of this lesson we will discuss wind generated waves and what we mean by a 'fully-developed' sea.
When
wind blows over the ocean, surface waves are generated by
transferring some of the wind's energy, in the form of momentum, from
the air to the water. In reality, the simple sine wave of the ideal
wave we discussed in Part 1 is not realized in the ocean - as we also
discussed in Part 1, the actual sea surface is made up of component
waves with different periods and heights. In a large storm, component
waves of many different wavelengths and directions are being
generated simultaneously and they combine, by the process of
interference, to create "sea", a very
chaotic state of the sea surface that has no discernible
organization. Waves in this
"sea" show no consistent direction nor wavelength or period. If you
are drifting stationary on a ship at sea and try, for instance, to
determine the period of an approaching wave by measuring the time it
takes two success crests to pass the bow, you get frustrated because
the crest you are tracking suddenly disappears
(destructive interference) only
to reappear (constructive
interference) at some distance away (this is a process of
wave interference that is shown graphically in Fig. 10.15 above).
Over time the energy from the storm generates larger and larger waves
that begin to gain some organization as they move away from the
active generation area as
"swell"
as we discovered in Part 1 of this lesson, and as shown
there and in the book as Fig. 10.11.
Because the 'sea' is made up of many component waves with different periods and heights (and not a single monochromatic or single period wave) we monitor the growth of 'seas' not by the growth of an individual wave, but by the growth of the sea's wave spectrum (a statistical property that describes ALL of the component waves present in the sea). As you can see in the figure below, this ocean wave spectrum has two major features. The:
How big these wind waves get is dependent upon four variables:
For a given constant wind speed, if the depth, fetch and duration are large enough (the minimum required values of each), the waves that consititue the 'sea' will reach what is called "full-development", where the largest of the waves in the 'sea' cannot grow any larger and its wave height and wavelength has reached its full potential. Usually, we ignore depth in our discussion of full development; so I will concentrate on fetch and duration.
If a sea is fully developed for a given constant wind speeed, it will not continue to grow even when the fetch or duration is more than the minimum required for full development.
As we learned earlier, wave steepness of an ideal wave is measured by the "steepness parameter", H/L, which increases as H increases or as L decreases. According to wave theory, when H/L > 1/7, waves become too steep and unstable, so they break (Fig. 10.17); therefore, H/L > 1/7 is called the "breaking criteria". In a many-component wave sea, however, H and L are statistical parameters calculated from the spectra; so even though they still obey the breaking criteria, the definition is slightly different.
I would like to give you an example of two different H and L combinations to demonstrate what the steepness parameter represents: Suppose a sea was fully developed for a low wind speed and had the values H = 2 m and L = 14 m. Therefore H/L would be 2/14 or 1/7 (exactly at the breaking criteria). Suppose another fully developed sea was reached for a higher wind speed and had values of H = 4 m and L = 28 m. In this case, H/L would be 4/28 or 1/7 (again exactly at the breaking criteria). In other words, in both cases the seas were fully-developed, yet for the higher wind, H and L were twice as big as for the slower wind. See Fig. 10.14.
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Fully Developed Sea |
As you can see in the table below, as wind speed increases, full development results in larger and larger values of H and L and require longer and longer maximum fetch and duration. For instance, for several wind speeds given below, note how large the fetch and duration must become, and how large H and L become when full development is reached. The values for H, L and T are average values or derived values from the spectra.
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From the table note that for a wind speed of 40 km/hr, for instance,when fetch is less than 176 km, or when duration is less than 11.5 hrs, the seas will not become fully developed -- we say, in this case, that the fetch and duration "limit" full development.
As an aside, note from the table above that as wind speed increases so does the 'size' of the sea (wave height and period/length of the individual waves get progressively larger) -- so we can conclude that full development at a given wind speed will not be fully developed if we increase wind speed. This increase in speed requires a longer fetch and duration to produce 'bigger' waves, and will result in a new state of full development.
Water depth also may be limiting, because if water is too shallow, the wave steepness will grow more than is warranted by the fetch and duration, and the breaking criteria will be reached before the waves are fully developed.
Even after the sea are fully developed, the wind may continue to transfer momentum to the ocean but, because the waves cannot grow any larger (they are fully developed), the excess energy supplied by the wind must be dissipated. This dissipation occurs when the waves break and, through the turbulent dissipation of energy, "white-caps" are created. Unlike "surf", which we will discuss in Part 3 of this lesson, these open-ocean, deep-water breakers are NOT caused by decreasing water depth, but because they are dissipating energy (the wave is too steep), and because excess energy must be dissipated.
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White caps - why and how they are generated |
Oceanographers determine the minimum fetch and duration required for full-development for a given wind speed in carefully controlled experiments, where progressive increases in the wave energy spectra are calculated and compared.
The main concept to understand in these experiments is that when fetch and/or duration are large enough for a sea to be fully developed, there will be no additional growth in the wave spectra, regardless of whether fetch or duration increase beyond that point.
The other important point is that full development depends on two variables (fetch and duration) so, to determine the effect that one of those variables has on full development, we have to 'neutralize' the other. Let me give you an example. Recall that we learned that the conductivity of of seawater was directly proportional to both temperature and salinity. Our objective was to use conductivity as a precise means of determining the salinity; therefore, we had to hold the temperature constant (usually at 20 C). We don't hold fetch or duration constant in the same way as we do for conductivity, however. If our goal is measure the minimum fetch required for full development, we must allow the wind to blow at least as long as the theoretical minimum duration required for full development; and if our goal is to measure minimum duration, we must place our wave gauge at a distance as least as great as the minium fetch required for full development.
To see how this is done for wave fetch, consider the following set up (note in the graph below that I am using two different figures: the one on the left is a plan view of the coast and the ocean; the one on the right is a plot of the progressive growth of the wave spectra as fetch increases).
Six wave gauges (numbered 1 through 6) are located at increasing distances away from a straight coastline, as shown on the plan view on the left hand side of the figure below. Then, for a steady wind that blows directly offshore for a long period of time (more than the minimum duration required to reach full development ), we measure wind wave growth at each gauge and compare their wave-energy spectra (as shown in the wave energy spectral plot on the right side of the figure below).
Note in the wave energy plot to the right above that, as the fetch increases, the spectral peaks shift toward longer periods and the total amount of wave energy (the area under the curve) increases. This continues until the spectral plot for wave gauge 6, which (to the limits of such measurements) we observe, has the same spectral peak period and the same amount of wave energy as wave gauge 5 (i.e., for all practical purposes 5 and 6 have the same spectra). We conclude that full development, and the minimum fetch required for full development, were reached at fetch 5 because there was no further growth in the spectrum at fetch 6. As I indicated earlier, this is a very important concept that you should understand (the spectra will not continue to grow at fetches longer that the minimum required for full development ).
Why is the required fetch not at wave gauge 6 or 4?
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Wave spectral growth - a discussion of the growth of the spectra |
Now that you have learned about the minimum required fetch, how would you set up the experiment to determine the minimum required duration?
To answer that question assume first that you place your wave qauge at a fetch that is greater than or equal to the minimum required fetch (in our example above, fetch 5 or 6). WHY?
Then assume that, initially, there is no wind and no resulting waves, and that the experiment begins when the wind begins to blow offshore at a constant speed. NOW WHAT WILL YOU MEASURE, and how will you know when you have reached the minimum duration required for full development? Hint: you also would use spectral growth, but now as a function of time, not distance. Do not confuse the labeling of the spectral plots for time, with the period of the x-axis.
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