9.5: Sea Development and Wave Height

As a wave’s height is built up by winds, its shape is modified from that of capillary waves. The shape first becomes close to the smooth sine wave form shown in Figure 9-2a,b. Subsequently, the crest and trough are modified progressively as the wave builds, and the wave shape becomes trochoidal (pointed crests and rounded troughs; Fig. 9-2c). As wind energy is absorbed by waves, their height, speed, period, and wavelength are increased.

Winds never blow uniformly over the water because they are highly variable in both time and space. Consequently, in the area where the waves are formed by the wind, waves of many different heights, wavelengths, and even directions of travel are present at the same time. Mariners refer to this confused state as a “sea.” In a “calm,” there are no significant waves, and the sea surface is flat. In a “swell”, waves are generally smooth, mostly of the same wavelength and from the same direction. How a sea becomes a swell is explained later in this chapter when we consider wave dispersion.

Waves sometimes break in deep water just as they do near the shore, but waves breaking in deep water are often called “whitecaps.” Waves break because they have become too steep. When the steepness of a deep-water wave (H/L) reaches 1:7 (wave height equals one-seventh of wavelength), the wave becomes unstable and the crest tumbles down the forward slope of the wave, creating a breaking wave. If winds are very strong, the tops of the largest waves may be blown off by the wind.

Waves break when they have reached their maximum possible height for the wind speed. They also break when seas are developing and the waves cannot be modified quickly enough to longer wavelengths and greater heights to absorb the energy introduced by the winds. As a wave becomes oversteepened and breaks, some of its energy is dissipated by turbulence, which releases heat. Consequently, this excess energy cannot be used to increase the wave height.

Factors Affecting Maximum Wave Heights

A sea is said to be fully developed when the amount of wave energy lost to turbulence in breaking waves is equal to the difference between the total energy input from winds and the amount of wind energy needed to maintain the sea. Waves of many different heights and periods are present in a fully developed sea, but storms with stronger winds produce waves with longer maximum periods than are produced by lower wind speeds (Fig. 9-7a,b). The maximum height of waves created by any specific storm or series of storms depends on the wind speed and the length of time the wind blows. The maximum height also depends on the wind fetch, which is the uninterrupted distance over which the wind blows (Fig. 9-7c). In shallow water (depth less than one-half of the wavelength), water depth is a limiting factor.

Figure 9-7. Relationships between wind speed, fetch, the length of time over which the wind blows, and the characteristics of the waves that are formed. (a) Strong (higher-speed) winds produce storms with greater total wave energy, and this energy is stored in waves of longer periods. (b) Strong winds also produce waves that have longer wavelengths and greater wave heights, provided that the winds blow long enough and have sufficient fetch. (c) The fetch is the distance over which the winds blow across the water to create waves. Fetch can be limited by the presence of a coastline or, where the storm is completely over water, by the dimensions of the storm itself. (d) The maximum wave height that can be reached is limited by the fetch, and this maximum wave height is reached only if the winds blow for a sufficiently long time.

Figure 9-7d shows the effect of wind duration and fetch on maximum wave height. As the wind begins to blow, waves accumulate energy from the wind. Wave height initially increases rapidly, then at a progressively slower rate. However, if the fetch is small, the maximum wave height is limited because waves relatively quickly travel out of the area where the wind is blowing. We can see the effects of a small fetch in lakes or in harbors protected from ocean waves. The fetch is restricted in such areas because the waves encounter a shoreline. No matter how strong winds are or how long they blow, only small waves can be created in harbors and all but the largest lakes.

The highest ocean waves are created where winds are strong and blow persistently over long fetches. High waves can also be generated when a series of strong storms passes in the same direction across the same fetch over a period of several days or longer. In this situation, some of the shorter-wavelength waves created by one storm do not have time to travel out of the area before the next storm arrives. Each successive storm simply builds on the height of waves remaining from preceding storms.

Maximum Observed Wave Heights

Persistent winds and storm tracks are arranged in bands with an east-west orientation (Chap. 7). Therefore, calm regions alternate with stormy regions from north to south in the oceans. The calm regions limit the fetch that can occur in a north or south direction in the ocean basins, but that does not mean that waves travel only east or west. First, the trade winds and westerly winds in the east-west wind bands do not blow directly east or west. Second, storms produce rotating winds and, thus, winds and waves of all directions. Third, if waves encounter a landmass or reef, the direction of wave travel may be altered as discussed later in this chapter.

Not surprisingly, high waves are most common in the Pacific Ocean because the Atlantic and Indian Oceans are much narrower and provide a more limited fetch. The longest fetches are within a band of westerly winds stretching around Antarctica. 

A giant wave at least 34 m high was measured by the U.S. Navy vessel Ramapo on 7 February 1933 in the tropical North Pacific Ocean. In 1998, a wave estimated at nearly 43 m high was measured during the Sydney to Hobart yacht race in the South Pacific Ocean. Although these were the largest waves reliably reported, higher waves undoubtedly occur from time to time. It is not surprising that such extremely high waves have not been measured, since any sailor whose vessel is faced with a 30-m or higher wave has many concerns other than measuring wave height. Most vessels would survive the ride through even the highest wave unless the wave was extremely steep-sided and breaking. A 30-m-high steep-sided wave breaking over the deck of even the largest ocean vessel may be the last wave the vessel ever encounters. Indeed, such large waves may have caused the disappearance of many ships in the past.

So far, the highest waves reliably reported in the Atlantic and Indian Oceans were about 15 m high. However, in September of 2004, the center of Hurricane Ivan passed directly over six tide/wave gauges mounted at depths of 60 to 90 m on the Gulf of America (Golfo de México) continental shelf. The highest wave measured by these gauges was 27.7 m. The area of highest winds within Ivan did not pass directly over any of the gauges, and it was calculated that the highest wave generated by this storm may have exceeded 40 m. Satellites such as the TOPEX/Poseidon satellite can measure ocean surface heights to an accuracy of within less than 5 cm. Unfortunately, these sensors cannot yet measure the heights of individual waves because the width of their measurement beams is large compared to the distance between ocean wind waves.

Effects of Currents on Wave Height

Steep-sided waves can be created when waves travel in the direction opposite that of a strong ocean current. The opposition of current and wave motion shortens the wavelength of the waves and increases their steepness, particularly on the front face of the wave. This effect is illustrated in Figure 9-8.

Figure 9-8. (a) Waves from around Antarctica travel northward and meet the strong, southward-flowing Agulhas Current. (b) As each wave encounters the current, its forward speed is decreased because the current moves surface water southward, and water particles in each wave are a little farther south after each wave orbit, instead of in their original position. As each wave slows, the following wave that has not yet encountered the current is not slowed, so its crest becomes closer to the crest of the wave preceding it. Hence, wavelength decreases and steepness increases as the figure shows. (c) The tanker World Glory, sinking after breaking its back in waves steepened by the Agulhas Current.

In extreme cases, waves can have almost vertical faces. Long-wavelength waves travel faster than vessels. When a vessel encounters a large wave with a nearly vertical face, the vessel may be unable to climb up and over the wave rapidly enough to avoid what is often a fatal plunge under the wave.

Such steep waves occur often in some areas, including where the swift Agulhas Current flows south along the Indian Ocean coast of southern Africa (Fig. 9-8a, Chap. 8). Large waves built by Antarctic storms travel north into this area, which is a major shipping lane for traffic between the Indian and Atlantic Oceans and is heavily traveled by oil supertankers. Several ships have been severely damaged or sunk there due to the shortened and steepened waves. In 1968, for example, the tanker World Glory broke in two, spilled its entire cargo, consisting of 14 million gallons of oil, and sank after encountering such a wave (Fig. 9-8c).

Tankers are constructed with most of the hull weight concentrated in the engine room and crew quarters at the stern, and the anchor-handling and other equipment in the bow. In the middle of the ship, oil is stored in separate compartments held together relatively weakly by the hull. A tanker can break in the middle if it becomes suspended with its center section on the crest of a high, steep-sided wave or suspended between two waves with the bow section on one wave and the stern on the other. Sophisticated satellite-based radar and other sensors now provide accurate advanced wave height forecasts in areas such as the Agulhas Current, so vessels are now able to avoid this region when dangerous waves are likely to be present.

Are Wave Heights Increasing?

Higher waves possess higher energy than lower waves and can create more damage when they impact a shoreline. Therefore, it is important to know whether wave heights are increasing due to higher wind speeds caused by a changing climate. However, measuring wave heights is not as simple as just recording the maximum wave height at one location over a period of time. Generally, oceanographers measure a parameter called “significant wave height,” which is a measure of the average height of approximately the highest one-third of all waves within a given area at a specific time. Methods of measuring wave heights have varied in the past several decades, so there are very few long time-series records of wave heights measured by a consistent method. This lack of consistent methodology makes conclusions about long-term trends in wave height difficult.

Wave heights in the North Atlantic Ocean were measured by researchers on a lightship moored off the southwest tip of England during 1960–1985. These measurements showed not only that the maximum wave heights vary widely between years, but also that the maximum wave heights apparently increased from about 12 m to about 15 m, about 25%, over this 25-year period. Since 1985, similar increases in wave heights have been observed in other parts of the Atlantic and Pacific Oceans by other techniques, including measurements of significant wave height by satellite-based sensors, calculation of significant wave heights from historical wind data records, and seismological data. Seismological data can be used because the microscale fluctuations in seismic records are related to the impact of waves on the coastline.

Although wave-height studies have shown that wave heights are increasing in some areas of the Atlantic and Pacific Oceans, they have also shown that wave heights have not increased significantly in other areas of these same oceans. At present, we do not know whether a long-term trend toward higher maximum wave heights is real. If it is real, we do not know whether it is related to climate change, whether the trend will continue, or in which areas this change is occurring. We are also unsure to what extent opposite trends or a lack of change may have occurred in other oceans.

However, we do know that any increase in maximum wave heights must be related to increased wind speeds, storm frequencies, or both. Small changes in ocean surface temperature may cause changes in the ocean-atmosphere interactions that create winds (Chap. 7). Hence, if wind speeds or storm frequencies have increased, the changes may be related to enhancement of the greenhouse effect caused by human release of greenhouse gases (CC9). Alternatively, the change in wave heights may be related to a natural long-term climatic cycle. Long-term climatic changes or cycles with periods of 30 years or more are known to occur. For example, historical records for Atlantic hurricanes suggest that they were fewer and weaker during the 1970s through the 1990s than in the preceding decades or in the current millennium (Chap. 7).

Considerably more information will be needed to fully identify the trends in wave heights and to determine whether these trends are part of a natural climatic cycle, are related entirely to the greenhouse effect (CC9), or are partially natural and partially related to the greenhouse effect. These issues are important because any long-term trend of increasing wave heights will pose problems for ships and increase coastal erosion.