Читать книгу Waves and Beaches - Kim McCoy - Страница 31

Waves in a sea do not have the regular and precise properties of waves generated in a wave channel. In a sea, the height of the crests and the depths of the troughs are irregular, and the length of each crest is short. These waves are individual hillocks of water with changing shapes that move independently. The limits of a wave in a sea are indefinable; each mass of water that the eye selects as a wave has a different shape, a different speed, and a slightly different direction from the other waves in the sea. The words period, velocity, and wave length have lost the meaning they had in the orderly environment of the wave channel. Try to determine the wave length of the waves in the photo on page 70. The spacing between waves is exceedingly irregular and demonstrates why statistical methods must be used to describe the properties of waves in a sea. Wave heights are nearly as irregular, but fortunately waves rise from a ready reference (the mean sea level) and there is somewhat less difficulty in defining wave height. For descriptive purposes, it is customary to use the average of the highest one-third of the waves (the significant wave height, H_⅓, see figure 13). The average of the highest one-tenth of the waves is sometimes noted as .

Under harsh conditions, waves can become so irregular and jumbled they are said to be “confused,” with no recognizable height or length. Newhaven, East Sussex, United Kingdom. Suerob/iStock

FIGURE 13: Wave heights and wind speeds observed in the North Atlantic (70,000 observations).

FIGURE 14: The sum of many simple sine waves makes a sea.

Thus a sea is the result of superimposing a number of sinusoidal wave trains one on top of another, as shown in the accompanying conceptual diagram figure 14 above. Each layer represents a series of regular sine waves, as alike as those on a sheet of corrugated roof material, and has its own characteristic height, wave length, and direction. Individually the waves in these trains are as true to their classical formulas as those in the model tank.

The real instantaneous sea surface at any point is made up of all these layers added together. Where a number of crests coincide, there will be a high mound of water—but it will not last long, for the component waves soon go their own way. Similarly, a coincidence of troughs creates an unusually low spot, also of short duration.

FIGURE 15: The wave spectrum for fully developed seas caused by winds of 20, 30, and 40 knots.

Since there are small wave crests in the large troughs and small depressions in the tops of the high mounds, on average the troughs and crests of the many layers of waves tend to cancel themselves out. The more layers of waves, the more random the sea surface and the lower the average wave height.

The need to reduce these complicated irregularities to a form that would be usable by the Navy in wave forecasting led scientists in the 1940s to a method of describing waves by means of their energy spectra. In this scheme a value is assigned to the square of the wave height for each frequency and direction. Then, after the portion of the spectrum where the energy is concentrated has been determined, it is possible to approximate average periods and lengths for use in wave forecasting. In other words, a wave spectrum gives a statistical description of wave energy and how it is distributed among various wave periods.

Some of the properties of wind waves are illustrated by figure 15, in which wave period is plotted against the amount of energy contained for three wind velocities. Each curve (or spectrum) represents the distribution of energy between various periods in a fully developed sea; the area under each curve represents the total energy. Consider first the 20-knot wind (a knot is a nautical mile per hour and thus equals 1.15 mph or 1.85 km/h). This relatively modest wind raises waves whose average height is 5 feet (1.5 m) and whose energy is spread over a band of periods ranging from seven to ten seconds.

If the wind increases to 30 knots, the waves become substantially higher and the periods longer. There is more energy available and these longer waves store it better. Now the average height is 13.6 feet (4.1 m), and the maximum energy is centered around a period of twelve seconds.

The upper curve of energy for the 40-knot wind waves shows a sharp peak at 16.2 seconds; the average height of the waves has increased to 28 feet (8.5 m).

Two things are clearly evident: As the wind velocity increases, (1) the amount of energy that can be stored by the waves increases greatly (this is because the waves are much higher and the energy is proportional to the square of the wave height), and (2) the periods become longer. (Note that in many scientific papers dealing with waves, the period, T, has been replaced by its inverse, frequency. Thus f = 1/T and a ten-second wave has a frequency of 0.1 Hz.)

Table 3.1 gives the most important characteristics of seas that are fully developed for winds of various velocities. For example, a 20-knot wind must blow for at least ten hours along a minimum fetch length of 75 miles (120 km) to raise fully the waves it is capable of generating. When the sea from a 20-knot wind is fully developed, the average height of the highest 10 percent of the waves will be 10 feet (3 m). If a 50-knot wind were to blow for three days over a 1,500-mile (2,400-km) fetch, the highest tenth of the waves would average about 100 feet (30 m) high. Fortunately for ships, storms rarely reach such dimensions or durations, and we have refined our wave forecasting.

TABLE 3.1 Conditions in Fully Developed Seas

Wave forecasting evolved during World War II and was refined throughout the world in the 1950s and 1960s. By the 1970s, the US Navy’s Fleet Numerical Meteorology and Oceanography Center (FNMOC) had developed a spectral wave ocean model (SWOM). In the 1980s, the Helmholtz-Zentrum, in Geesthacht, Germany, developed another wave model called WAM (short for Wave Modeling). The British Oceanographic Data Centre has similar models and maintains an impressive amount of marine data, as does the Scripps Institution of Oceanography Coastal Data Information Program (CDIP), which provides coastal environmental data, wave models, and forecasting. Today, wave forecasting around the world is routinely used for optimizing military, cargo, and cruise ship routing. Proper routing reduces wave damage to vessels and fuel consumption. The ship captain, coastal engineer, beach researcher, and millions of surfers all rely upon the output from daily wave forecasting models. Kiss your wave forecaster.

Even in storms with lower-velocity winds there is always a statistical chance of a very high wave, called a rogue or extreme wave. No one can predict when or where or how high, but super-waves must exist because of the random nature of waves. For example, if 1,000 waves were observed on 20 different occasions, on one of those occasions the highest of the thousand waves will be 2.22 times the significant height. Thus, if the significant height were 44 feet (13.4 m), as it would be in a fully developed 40-knot sea, the “statistically exceptionally high wave” could be 97 feet (30 m) high.

The unfortunate bow of the aircraft carrier USS Bennington after encountering angry storm waves in a typhoon off Okinawa, Japan, in early 1945. The steel deck is 54 feet (16 m) above the waterline. US Navy

Such a wave could exist only momentarily in a storm and it would be very unstable. It would tower over twice as high above most of its fellow waves, reaching upward into a mass of air moving at 40 knots. The crest would then be blown off, forming a breaking wave in deep water. It is these breaking storm waves—and they need not be super-waves necessarily—that do serious damage to the ships that are unlucky enough to be hit. The thousands of tons of violently moving water contained in the torn-off crest of even a moderate-size breaking ocean wave can destroy the superstructure of a ship.

The vast difference in the destructive power of breaking and non-breaking waves in deep water is worth examination, because it illuminates a fundamental property of waves. Objects in the water, such as ships, tend to make the same motion as the water they displace. A ship at sea in large waves will describe orbital circles that are roughly the same size as the water in that part of the wave. There is little relative motion between the bulk of the ship and the surrounding water. This motion of a ship may be uncomfortable, but it is safe (see figure 16).

FIGURE 16: On top, ship and water particles in a large, nonbreaking wave have orbits of about the same size, so there is little motion relative to one another. On the bottom, water at the crest of a large wave has broken free of the orbit and will collide violently with the ship.

If the crest breaks off a wave, however, the water moves faster than the waveform and independently of the orbiting water (and ship). The collision between the two could prove disastrous.