1
The Calm Sea

Once, as I was sailing from Marina Del Rey, California, to Baja California, Mexico, the fickle morning wind slowly diminished and disappeared by noon. The sea took on a glassy sheen, marred by nothing but the faint trace of a southerly current. The sails hung listlessly, barely moving with the slight roll of the boat. Dreams, my 33-foot-long, cutter-rigged sailboat, was becalmed.1 My charts put us a little south and east of Sixty Mile Bank, an area of submarine mountain ranges and deep canyons—a favored destination for fishing boats operating out of San Diego. It was a warm day, and after trailing a line astern for the safety of the swimmers, some of the crew went overboard for a refreshing swim in midocean, around 54 nautical miles from the nearest land, then returned to await the coming of the afternoon breeze.

As flat as the sea was that memorable day, there is in fact no such thing as a perfectly calm sea. In the absence of any other disturbing force, planetary gravitational forces are constantly at work on the earth’s oceans. Newton’s law of universal gravitation tells us that there is a mutual attraction between two bodies. In the case of the earth, the situation is more complicated, since it involves forces between the



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Extreme Waves 1 The Calm Sea Once, as I was sailing from Marina Del Rey, California, to Baja California, Mexico, the fickle morning wind slowly diminished and disappeared by noon. The sea took on a glassy sheen, marred by nothing but the faint trace of a southerly current. The sails hung listlessly, barely moving with the slight roll of the boat. Dreams, my 33-foot-long, cutter-rigged sailboat, was becalmed.1 My charts put us a little south and east of Sixty Mile Bank, an area of submarine mountain ranges and deep canyons—a favored destination for fishing boats operating out of San Diego. It was a warm day, and after trailing a line astern for the safety of the swimmers, some of the crew went overboard for a refreshing swim in midocean, around 54 nautical miles from the nearest land, then returned to await the coming of the afternoon breeze. As flat as the sea was that memorable day, there is in fact no such thing as a perfectly calm sea. In the absence of any other disturbing force, planetary gravitational forces are constantly at work on the earth’s oceans. Newton’s law of universal gravitation tells us that there is a mutual attraction between two bodies. In the case of the earth, the situation is more complicated, since it involves forces between the

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Extreme Waves earth, sun, and moon; and even more distant planets have a small, albeit negligible, effect. These attractive forces are strong enough to move mountains and exert a measurable effect on oceans, tugging the water one way when the sun and moon are close and the force is greater, tugging it another way as the force is relaxed or moves to another part of the sea. Since water is a fluid, if it rises at one point, it must lower elsewhere, causing a current to flow from one point to the other. If left undisturbed, any body of water will eventually settle into a stable configuration with a flat surface. The surface tension of the fluid acts to preserve that stability. It is only in the presence of some disturbing force that the surface begins to change shape. WAVE TYPES Wind is the usual disturbing force, producing wind-generated waves, the waves most commonly experienced. Oceanographers distinguish six major types of waves, typically categorized in terms of increasing period (Figure 1). These are capillary waves, which have periods of a fraction of a second; ultragravity waves, which have periods ranging from 0.1 to 1 second; gravity waves, 1 to 30 seconds; infragravity waves, 30 seconds to 5 minutes; long-period waves, 5 minutes to 24 hours; and transtidal waves, 24 hours or longer. In terms of the topic of this book, wind-generated gravity waves are the most likely source of extreme waves, but the next category, long-period waves, can also produce extremely dangerous and damaging waves. Gravity waves—the name arises from the fact that wind piles water up, but gravity pulls it back down—are further subdivided into seas and swell. Seas—wind-driven waves—usually have shorter periods and are of greater significance to the mariner. Swell—a succession of waves that have moved beyond the immediate influence of the wind that caused them—have longer periods (10 to 30 seconds), but there are overlaps and no distinct dividing line between periods. Because the wavelength of swell is usually long compared to the length of a vessel, it generally does not concern the mariner in the open ocean. When the swell is large and its wavelength close to the length of a vessel, it is a different matter.

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Extreme Waves FIGURE 1 Types of ocean waves. Other natural forces can disturb the equilibrium of the sea surface, wind being only one of them. These forces may be as small as the wake of a passing ship or as large as the great currents that circulate through all of the major oceans, the horrifying force of major storms, undersea earthquakes and landslides, and the tides themselves. WAVE PROPERTIES Some of these forces primarily affect the surface of the oceans, which is of great importance, of course, because it is where most human activity takes place at sea. Still others can move a body of water extending all the way from the bottom of the sea to the surface, and this difference is of vital importance when such disturbances approach shallow water. An important parameter for describing waves is the wavelength, L, which is simply the distance between two successive wave crests or peaks. The ideal wave can be visualized as a sine wave—that is, having the same shape that can be produced by tying a rope to a tree and shaking the free end up and down vigorously, causing a series of S-shaped waves to travel down the rope. Such motion is described by three properties: in addition to the wavelength, there is the wave height, H, the height of the crest above the trough, and the wave period, T, the time it takes to make one complete cycle. Sometimes the wave amplitude, A, is used; this is the distance from the centerline to the crest. A is equal to one-half H for the ideal wave. Whenever wave height is men-

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Extreme Waves tioned in this book, it will refer to H, the crest-to-trough distance. The period is the time in seconds for one complete cycle of a wave—that is, from one crest to the next. The wave speed, c, is also of interest. It is equal to the wavelength divided by the period—that is, the distance traveled divided by the time it takes to travel. Alternatively, we can write: Wavelength = Period × Wave Speed. This is a fundamental relationship that applies to many different kinds of waves, including light, radio, electrical, and sound. The main features of a wave are summarized in Figure 2. In deep water, the speed of the wave is independent of depth and is determined only by the period. Thus, a wave with a period of 12 seconds and a wavelength of 750 feet will have a speed of 750/12 = 62.5 feet per second (37 knots). As this same wave moves into shallow water, its speed depends on the depth of the water. For example, if the water depth is 11 fathoms (66 feet), the wave speed is 27.2 knots, but when the depth is 5.5 fathoms (33 feet), the wave speed drops to 19.3 knots, and so on. As the wave slows, its height builds. Consequently, shallow water affects both the height and the speed of a wave—a most important thing to remember. The energy carried by a given set of waves is proportional to the wave height squared. There are more exact equations, but we need not be concerned with them. It is sufficient to know that local newspapers run articles when winter storms bring waves 10 feet high to the beaches in Newport Beach, California, where I live. Yet a 100-foot-high extreme wave packs 100 times as much destructive potential as the 10-foot- FIGURE 2 Properties of an ideal wave.

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Extreme Waves high waves that we would find very impressive while watching the surf crashing ashore. Meteorological reports typically provide wave periods (T) and wave heights (H). The speed, period, and wavelength of an “ideal” wave are related mathematically. However, it should be understood that the periods and wave heights given in weather reports are “typical” values, meaning they represent the preponderance of waves of various sizes and periods that the mariner may encounter. Thus, the most likely height wave and the most likely period wave bear no mathematical relationship to each other. The wavelength is related to how fast waves travel but has another useful purpose as a measure of when water is deep for a particular wave. As a rule of thumb, oceanographers say that water is deep if the depth is greater than one-half a wavelength. Since the average depth of the oceans is around 2.5 miles (13,115 feet, or 4,000 meters), for most waves in the open ocean the water is deep and the effect of the wave does not extend more than 300 to 600 feet below the surface. A submarine at this depth would not sense the turbulent seas of a major storm above it; here the sea remains calm. However, there are certain waves—earthquake-produced waves known as tsunami, for example—that have very long wavelengths; thus, even midocean is considered “shallow” for these waves. The passage of such long-wavelength waves roils the entire sea, from the surface to the depths, but this is generally of no major consequence until the wave enters shallow coastal water, where it slows down and piles up into towering and destructive walls of water capable of sweeping all before them. Another important wave parameter is wave steepness. The steepness is a measure of how dangerous a wave can be. Thus, a very high wave with a short wavelength is said to be very steep. Wind or sea bottom conditions can increase steepness. In contrast, a high wave with a very long wavelength (such as an ocean swell) presents less of a threat to vessels since they can ride up and over the gradual slope. Theoretical studies of the idealized wave shown in Figure 2 indicate that there is a limit to the steepness of a wave traveling in deep water. Once the height of the wave reaches one-seventh of the wavelength, the wave is so steep that it will break.2

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Extreme Waves Back onboard Dreams, the view from Sixty Mile Bank revealed an endless expanse of blue water. We were too distant from land to view the shore; no passing boat interrupted our feeling of complete isolation on the fringe of the Pacific, the world’s largest ocean. The experience of floating in the calm sea that day brought to mind the beginning of life itself. OCEANS AND SEAS The primordial forces that created the earth and left nearly three-fourths of its surface covered by water made life possible. Liquid water is one of the features that differentiate the earth from the lifeless planets in our solar system. As large as the land surfaces may seem, they are dwarfed by the vast oceans and major seas of our planet, occupying 139 million square miles.3 (See Table 1.) The reach of the oceans is perhaps best visualized by realizing that the Pacific Ocean alone covers 32.4 percent of the earth’s surface, more than all of the landmasses combined. (Here, where we calmly floated during our journey from Marina Del Rey to Baja, we were a microscopic speck on the largest segment of the earth.) The Atlantic Ocean TABLE 1 The Earth’s Oceans and Seas Water body name Area (million square miles) Average depth (feet) Pacific Ocean 64.0 13,215 Atlantic Ocean 31.8 12,880 Indian Ocean 25.3 13,002 Arctic Ocean 5.44 3,953 Mediterranean Sea 1.15 4,688 Caribbean Sea 1.05 8,685 South China Sea 0.90 5,410 Bering Sea 0.88 5,075 Okhotsk Sea 0.61 2,749 Others 7.9 — Land 58 (29%) — TOTAL 197  

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Extreme Waves is the second largest of the great bodies of water, covering 16.2 percent of the earth, and the Indian Ocean is third, covering 14.4 percent. What, exactly, is an ocean? Oceans are vast bodies of saltwater that separate continents. Far to the west of us, after passing innumerable Pacific islands and remote atolls, the Pacific washes up on the shores of the continents of Asia and Australia. Although we commonly interchange the words “ocean” and “sea,” seas are in fact parts of oceans, but you must pass through some strait to reach them—the Strait of Gibraltar from the Atlantic Ocean to the Mediterranean Sea being one example. Or, farther south along the course we were pursuing, at the tip of Baja California lies the entrance to the Sea of Cortez. For roughly 5,000 years, people have ventured into the vastness of the oceans and seas, seeking food, trade, a new place to live—or just yielding to the urge to explore the unknown. As long as 4,500 years ago, the ancient Egyptians built vessels that traversed the Mediterranean Sea to places as distant as Lebanon to bring back lumber and other trade goods. And, from the earliest written records, the dangers inherent in the sea—storms and giant waves that crushed frail vessels—are evident. In The Odyssey, Homer (eighth century B.C.) describes how Odysseus, after offending Poseidon, god of the seas, witnesses his raft destroyed by a mighty wave:4 With that he rammed the clouds together—both hands clutching his trident—churned the waves into chaos, whipping all the gales from every quarter, shrouding over in thunderheads the earth and sea at once—and night swept down from the sky—East and South winds clashed and the raging West and North, sprung from the heavens, roiled heaving breakers up— …At that a massive wave came crashing down on his head, a terrific onslaught spinning his craft round and round—he was thrown clear of the decks— The story has a happy ending, however, because Ino, a sea nymph, takes pity on Odysseus and gives him her veil as a life jacket. He strips off his clothes and manages to swim to shore as his raft is lost. Unfortunately, the outcome for many other victims of ships struck by giant waves is not as happy; numerous ships have disappeared leaving no survivors, only pieces of floating debris to mark their demise.

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Extreme Waves A BRIEF HISTORY OF OCEAN EXPLORATION Despite the dangers, humans continued to explore the oceans for a thousand years beyond the time of Homer, staying close to shore at first, then gradually venturing farther and farther offshore, seduced by the traditionally calm waters and idyllic weather of the Mediterranean. In 1000 B.C. the Phoenicians took control of the Mediterranean and made it a Phoenician lake. If we believe Herodotus, a Phoenician crew was the first to circumnavigate Africa, taking three years to pass from the Red Sea, down the east coast, around the Cape of Good Hope, and back through the Straits of Gibraltar.5 From Scandinavia, Viking raiders reached England, France, and Spain, and traveled east to parts of Russia and coastal areas of the Baltic Sea. Piloting sturdy but light oceangoing vessels 60 to 80 feet long, they crossed the North Atlantic Ocean to Iceland and Greenland, and reached North America (Newfoundland) around A.D. 1000. At this same time, but half a world away, China was turning out the world’s best sailors and navigators. The Chinese developed paper, produced accurate nautical charts, used astronomy for navigation, and began to explore the South China Sea in the most reliable oceangoing vessels built up to that time.6 When Ming Dynasty Emperor Zhu Di came to power, he placed a man named Cheng Ho in charge of a shipbuilding program. At a shipyard in Nanking, Ho saw to the building of hundreds of vessels—some nearly 500 feet long—to create a Treasure Fleet that was to explore all of the known oceans and develop trade with foreign nations. Cheng Ho led seven expeditions between 1405 and 1433, traveling south to cross the Bay of Bengal, the Arabian Sea, and the Indian Ocean and, to the north, the East China Sea and the Sea of Japan. In the west, he reached the east coast of Africa, near the site of Mombassa, and in the northwest, he traversed the Red Sea as far as Mecca and into the Persian Gulf. He also visited Sumatra, Indonesia, Thailand, and Borneo. He chronicled rough seas and vessels lost on his voyages. In 1424, the emperor died and his successor closed the shipyard and idled the fleet. The Chinese withdrew into isolation. Arab traders took the place of the Chinese and by A.D. 1400 were in control of the trade routes and principal ports in the Indian Ocean.

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Extreme Waves Their range extended from the Red Sea and Persian Gulf south to eastern Africa and the Spice Islands, but they dared not venture into the unknown of the South Atlantic, due to the fearsome waves of the Agulhas Current. Meanwhile, first the Portuguese and then the Spanish were exploring southward, establishing bases along the west coast of Africa, and in 1488 Bartolomeu Diaz rounded the Cape of Good Hope. This set the stage for Vasco da Gama to round the Cape and finally reach India (1498), in an effort to reduce dependence on Arab traders for spices and other valued products from the Orient. Portuguese success led to Spanish concerns that the Portuguese would dominate the lucrative trade with east Asia, and eventually prepared the way for Columbus to prevail in his quest for royal approval of a voyage west—the “backdoor” route to the Spice Islands and the riches of the Orient. DISCOVERERS OF NEW WORLDS—COLUMBUS AND MAGELLAN Along with his discovery of the New World was Christopher Columbus’s great achievement of recognizing that there was something different about the winds that originated around the Canary Islands. Here were winds that were westerly and constant, as opposed to the variable winds encountered sailing down the coast. Without realizing it, Columbus had discovered the Northeast Trade Winds.7 Columbus’s passage across the Atlantic was remarkable. His log shows days of steady sailing at speeds of 6, 8, and even 10 knots through calm seas. No major storms were encountered. Columbus knew that he could return to Spain by first sailing northeast to catch the westerlies—the winds that blew east across the Atlantic, and that is exactly what he did. Fernão Magalhães (Magellan) was Portuguese and, like Columbus, sought the support of Spain when Portugal refused to support his grand plan to go east by sailing west. Eventually he secured the support needed, and on September 20, 1519, he sailed from Spain into the Atlantic with a fleet of five vessels, known thereafter as the Armada de Molucca. Six months later, battered by recurring storms and waves that

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Extreme Waves had nearly sunk the fleet, and realizing he could not find the magical strait to the Spice Islands before winter fell on his fleet in its full fury, he resolved to find a safe place to spend the winter. This turned out to be a protected harbor near the tip of Argentina, known today as Puerto San Julian. Besides weather, Magellan was challenged by mutiny, lost one ship in a storm, and had another ship desert and return to Spain. The remaining three vessels eventually traversed the strait that bears his name and made it across the Pacific, reaching Guam on March 6, 1521. A year and a half later—on September 6, 1522—a heavily damaged vessel was observed approaching southern Spain. It was the Victoria, the last of Magellan’s ships, his remaining crew finally making it home to tell the story of his epoch voyage. The other two ships had been lost in storms; Magellan himself had been killed and buried in the Philippines, the victim of an ill-advised fight with natives. The 18 surviving crewmen on the Victoria could claim the first circumnavigation of the world. Not only that, as proof of Magellan’s acumen, they unloaded a cargo of 381 sacks of cloves, sufficient to make the trip profitable despite the loss of three vessels.8 Today, the oceans continue to serve as a vital component of human existence, not only as means of transport and sources of food, but more importantly as essential elements of the earth’s climate control system, which makes the planet habitable. Water fills in deep canyons and broad plains, except in those areas where the continents or islands extend above the surface. The deepest points of the oceans surpass the highest points on land. The Challenger Deep, in the Philippine Sea, lies an incredible 36,000 feet (nearly 7 miles) below the surface of the sea! By comparison, Mount Everest, the highest point on land, is only 29,055 feet high. MODELING WAVES With the discovery of new worlds and the growing importance of maritime trade, better understanding of wind, waves, and weather took on new importance. Certainly the earliest shipbuilders concerned themselves with staying afloat, constructing vessels that would not swamp

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Extreme Waves easily, and developing these vessels by a process of trial and error. As sailing vessels became larger and more complex, shipbuilders had to consider the impact of waves, but more importantly, they had to consider the impact of wind. There was little reason other than scientific curiosity to try to understand the processes by which waves form and travel across the ocean. In the 1800s, some early work was done by George G. Stokes (1819-1903), an Irish-born mathematician and physicist. But it was not until the time of the Second World War that more serious efforts began. As the war turned the oceans into vast battlegrounds, understanding waves suddenly assumed new importance. Not only were battles fought in places and at times in which nature was as much an adversary as the enemy, it became necessary to land troops on islands and beaches in the Pacific and in Normandy. This was difficult enough in flimsy vessels in the face of enemy fire, but in rough seas it became exponentially hazardous. The earliest attempts to model wave actions in the ocean used the approximation that waves are sinusoidal—the idealized wave discussed at the beginning of this chapter and portrayed in Figure 2. At this point it is important to state that there are no such idealized waves in the sea. The sea is always in a chaotic state, the actual surface motion being a composite of hundreds of waveforms that have been reflected and refracted by distant islands or landmasses, intersecting and diverging to form a complex surface on which no two waves are the same. The next effort to represent realistic wave patterns was to consider waves as the sum of many idealized waves. In this approach, a number of sinusoidal waves with different heights and wavelengths were combined. This method enabled oceanographers to reproduce complex wave shapes, but it still falls short of serving as a tool that will work under all conditions—deep and shallow water, small and large waves. Now we know that it is possible to speak of realistic waves only in terms of statistical averages. For this reason, wave heights are reported as the significant wave height, Hs, and meteorological reports typically give the dominant period. The significant wave height is defined as the average height of the largest one-third of the waves, for a representative group of waves, and the dominant period is the period occurring most frequently in a group of waves. For the purposes of this book, I must

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Extreme Waves define one other term: a wave abnormally much higher than the significant wave, which I call an extreme wave, Hext. During the Second World War it became important to understand not only how waves form and move, but also the link between various sea conditions and waves so that wave heights and periods could be forecast. In the early stages of the conflict, the U.S. Navy commissioned Harald Ulrik Sverdrup, the director of the Scripps Institution of Oceanography, and Walter Heinrich Munk, a researcher at the Scripps Institution, to come up with an answer to this problem. Their initial effort considered ocean waves as periodic motion, represented mathematically as the sine waves described earlier in this chapter. A number of assumptions must be made for this approach to be valid. One is that the amplitude of the waves is very small and that waves are unchanged as they propagate. This method also assumes that all waves are identical at one point in time. It does not take much observation to understand that the conditions discussed above are rarely if ever encountered in the ocean, as Blair Kinsman points out in his classic work Wind Waves.9 Instead, there are all manner of waves—some small, some larger, occasionally one much larger—and not all travel in the same direction or even at the same speed. Yet despite their randomness, ocean waves do exhibit certain regular or reoccurring patterns and are thus amenable to applying Fourier analysis techniques to model them. Jean Baptiste Joseph Fourier (1768-1830) was a French mathematician who discovered that any periodic function could be approximated by a series of sine waves. The opposite is also true; by applying a Fourier transform, a complex function can be broken down into its components. This mathematical process was invented by Fourier in the 1700s. He had accompanied Napoleon’s army to Egypt as a science adviser, saw the French win many victories, and then was stranded in Egypt when the British navy sank the French fleet at Alexandria. This was a classic battle in which the British used wind and wave to successfully attack the French fleet! Fourier eventually made his way back to France with the tattered remnants of the French army, and was happy to once again be a mathematician and teacher. He was not forgotten by Napoleon, however, who drafted him

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Extreme Waves to serve as prefect of the department of Isère. Fourier never sought this position, but given no choice in the matter, he did a commendable job. In his spare time at Grenoble, he developed the details of his method for Fourier expansions and transformations. (See Chapter 3 for more details.) A similar process is used in earthquake studies. Seismometers measure how the ground moves as the waves generated by earthquakes pass through the earth. The resulting record, typically a squiggly line called a time history, shows how the earth moved at any point in time during an earthquake. If this record is digitized and analyzed using Fourier’s methods, a different type of graph is produced. The wave is broken down into component waves, and the resulting graph shows amplitudes of the components plotted versus frequency. This is useful because it shows at what frequency most of the earthquake energy is concentrated. If a nearby building has natural frequencies of vibration near the dominant ones in an earthquake, it will shake harder and more likely be damaged than if its frequency were different. Similar data can be gathered by recording instruments placed on buoys in the ocean or on offshore platforms. The time histories of waves can be converted to frequency spectra that show where most of the energy lies. The predominant frequencies can likewise be converted to a dominant or typical wave period. Like buildings, vessels have characteristic natural frequencies that depend on their size and method of construction. When these frequencies are close to wave frequencies, the vessel will roll or pitch more, sometimes to the point of capsizing. The next refinement in wind-wave theory was to recognize that due to the randomness of waves, probabilistic methods of analysis were necessary to make more accurate forecasts of wave heights and frequency of occurrence.10 Today, many improvements have been made in the mathematical models. Oceanographers are collecting wave data at sea to check the mathematical models and, in some cases, are using wave channels (analogous to wind tunnels) capable of creating artificial waves in the laboratory. Still, there is a lack of measurements on extreme waves. Some records have been obtained, but because giant waves occur infrequently and without warning, as well as the sheer difficulty of making measurements in huge seas when people’s lives are at stake, the amount of actual data is small.

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Extreme Waves Fortunately, where we drifted near Sixty Mile Bank that day, big waves—especially extreme waves—were not a consideration. The hurricane season was over and we did not expect any bad weather. Calm seas have a certain peacefulness, but being becalmed soon makes a sailor anxious. Eager to be under way, we searched for signs of wind.