# CHAPTER 32 WAVES, BREAKERS AND SURF
## OCEAN WAVES
### 3200. Introduction

Ocean waves, the most easily observed phenomenon at sea, are probably the least understood by the average seaman. More than any other single factor, ocean waves are likely to cause a navigator to change course or speed to avoid damage to ship and cargo. Wind-generated ocean waves have been measured at more than 100 feet high, and tsunamis, caused by earthquakes, far higher. A mariner with knowledge of basic facts concerning waves is able to use them to his advantage, avoid hazardous conditions, and operate with a minimum of danger if such conditions cannot be avoided. See Chapter 37, Weather Routing, for details on how to avoid areas of severe waves.

### 3201. Causes of Waves

Waves on the surface of the sea are caused principally by wind, but other factors, such as submarine earthquakes, volcanic eruptions, and the tide, also cause waves. If a breeze of less than 2 knots starts to blow across smooth water, small wavelets called ripples form almost instantaneously. When the breeze dies, the ripples disappear as suddenly as they formed, the level surface being restored by surface tension of the water. If the wind speed exceeds 2 knots, more stable gravity waves gradually form, and progress with the wind. While the generating wind blows, the resulting waves may be referred to as sea. When the wind stops or changes direction, waves that continue on without relation to local winds are called swell. Unlike wind and current, waves are not deflected appreciably by the rotation of the Earth, but move in the direction in which the generating wind blows. When this wind ceases, friction and spreading cause the waves to be reduced in height, or attenuated, as they move. However, the reduction takes place so slowly that swell often continues until it reaches some obstruction, such as a shore. The Fleet Numerical Meteorology and Oceanography Center produces synoptic analyses and predictions of ocean wave heights using a spectral numerical model. The wave information consists of heights and directions for different periods and wavelengths. Verification of projected data has proven the model to be very good. Information from the model is provided to the U.S. Navy on a routine basis and is a vital input to the Optimum Track Ship Routing program.

### 3202. Wave Characteristics

Ocean waves are very nearly in the shape of an inverted cycloid, the figure formed by a point inside the rim of a wheel rolling along a level surface. This shape is shown in Figure 3202a. The highest parts of waves are called crests, and the intervening lowest parts, troughs. Since the crests are steeper and narrower than the troughs, the mean or still water level is a little lower than halfway between the crests and troughs. The vertical distance between trough and crest is called wave height, labeled H in Figure 3202a. The horizontal distance between successive crests, measured in the direction of travel, is called wavelength, labeled L. The time interval between passage of successive crests at a stationary point is called wave period (P). Wave height, length, and period depend upon a number of factors, such as the wind speed, the length of time it has blown, and its fetch (the straight distance it has traveled over the surface). Table 3202 indicates the relationship between wind speed, fetch, length of time the wind blows, wave height, and wave period in deep water. If the water is deeper than one-half the wavelength (L), this length in feet is theoretically related to period (P) in seconds by the formula: The actual value has been found to be a little less than this for swell, and about two-thirds the length determined by this formula for sea. When the waves leave the generating area and continue as free waves, the wavelength and period continue to increase, while the height decreases. The rate of change gradually decreases. The speed (S) of a free wave in deep water is nearly independent of its height or steepness. For swell, its Figure 3202a. A typical sea wave. L 5.12 P 2 = .
BEAUFORT NUMBER Fetch Fetch 3 4 5 6 7 8 9 10 11 T H P T H P T H P T H P T H P T H P T H P T H P T H P 10 4. 4 1. 8 2. 1 3. 7 2. 6 2. 4 3. 2 3. 5 2. 8 2. 7 5. 0 3. 1 2. 5 6. 0 3. 4 2. 3 7. 3 3. 9 2. 0 8. 0 4. 1 1. 9 10. 0 4. 2 1. 8 10. 0 5. 0 10 20 7. 1 2. 0 2. 5 6. 2 3. 2 2. 9 5. 4 4. 9 3. 3 4. 7 7. 0 3. 8 4. 2 8. 6 4. 3 3. 9 10. 0 4. 4 3. 5 12. 0 5. 0 3. 2 14. 0 5. 2 3. 0 16. 0 5. 9 20 30 9. 8 2. 0 2. 8 8. 3 3. 8 3. 3 7. 2 5. 8 3. 7 6. 2 8. 0 4. 2 5. 8 10. 0 4. 6 5. 2 12. 1 5. 0 4. 7 15. 8 5. 5 4. 4 18. 0 6. 0 4. 1 19. 8 6. 3 30 40 12. 0 2. 0 3. 0 10. 3 3. 9 3. 6 8. 9 6. 2 4. 1 7. 8 9. 0 4. 6 7. 1 11. 2 4. 9 6. 5 14. 0 5. 4 5. 8 17. 7 5. 9 5. 4 21. 0 6. 3 5. 1 22. 5 6. 7 40 50 14. 0 2. 0 3. 2 12. 4 4. 0 3. 8 11. 0 6. 5 4. 4 9. 1 9. 8 4. 8 8. 4 12. 2 5. 2 7. 7 15. 7 5. 6 6. 9 19. 8 6. 3 6. 4 23. 0 6. 7 6. 1 25. 0 7. 1 50 60 16. 0 2. 0 3. 5 14. 0 4. 0 4. 0 12. 0 6. 8 4. 6 10. 2 10. 3 5. 1 9. 6 13. 2 5. 5 8. 7 17. 0 6. 0 8. 0 21. 0 6. 5 7. 4 25. 0 7. 0 7. 0 27. 5 7. 5 60 70 18. 0 2. 0 3. 7 15. 8 4. 0 4. 1 13. 5 7. 0 4. 8 11. 9 10. 8 5. 4 10. 5 13. 9 5. 7 9. 9 18. 0 6. 4 9. 0 22. 5 6. 8 8. 3 26. 5 7. 3 7. 8 29. 5 7. 7 70 80 20. 0 2. 0 3. 8 17. 0 4. 0 4. 2 15. 0 7. 2 4. 9 13. 0 11. 0 5. 6 12. 0 14. 5 6. 0 11. 0 18. 9 6. 6 10. 0 24. 0 7. 1 9. 3 28. 0 7. 7 8. 6 31. 5 7. 9 80 90 23. 6 2. 0 3. 9 18. 8 4. 0 4. 3 16. 5 7. 3 5. 1 14. 1 11. 2 5. 8 13. 0 15. 0 6. 3 12. 0 20. 0 6. 7 11. 0 25. 0 7. 2 10. 2 30. 0 7. 9 9. 5 34. 0 8. 2 90 100 27. 1 2. 0 4. 0 20. 0 4. 0 4. 4 17. 5 7. 3 5. 3 15. 1 11. 4 6. 0 14. 0 15. 5 6. 5 12. 8 20. 5 6. 9 11. 9 26. 5 7. 6 11. 0 32. 0 8. 1 10. 3 35. 0 8. 5 100 120 31. 1 2. 0 4. 2 22. 4 4. 1 4. 7 20. 0 7. 8 5. 4 17. 0 11. 7 6. 2 15. 9 16. 0 6. 7 14. 5 21. 5 7. 3 13. 1 27. 5 7. 9 12. 3 33. 5 8. 4 11. 5 37. 5 8. 8 120 140 36. 6 2. 0 4. 5 25. 8 4. 2 4. 9 22. 5 7. 9 5. 8 19. 1 11. 9 6. 4 17. 6 16. 2 7. 0 16. 0 22. 0 7. 6 14. 8 29. 0 8. 3 13. 9 35. 5 8. 8 13. 0 40. 0 9. 2 140 160 43. 2 2. 0 4. 9 28. 4 4. 2 5. 2 24. 3 7. 9 6. 0 21. 1 12. 0 6. 6 19. 5 16. 5 7. 3 18. 0 23. 0 8. 0 16. 4 30. 5 8. 7 15. 1 37. 0 9. 1 14. 5 42. 5 9. 6 160 180 50. 0 2. 0 4. 9 30. 9 4. 3 5. 4 27. 0 8. 0 6. 2 23. 1 12. 1 6. 8 21. 3 17. 0 7. 5 19. 9 23. 5 8. 3 18. 0 31. 5 9. 0 16. 5 38. 5 9. 5 16. 0 44. 5 10. 0 180 200 33. 5 4. 3 5. 6 29. 0 8. 0 6. 4 25. 4 12. 2 7. 1 23. 1 17. 5 7. 7 21. 5 23. 5 8. 5 19. 3 32. 5 9. 2 18. 1 40. 0 9. 8 17. 1 46. 0 10. 3 200 220 36. 5 4. 4 5. 8 31. 1 8. 0 6. 6 27. 2 12. 3 7. 2 25. 0 17. 9 8. 0 22. 9 24. 0 8. 8 20. 9 34. 0 9. 6 19. 1 41. 5 10. 1 18. 2 47. 5 10. 6 220 240 39. 2 4. 4 5. 9 33. 1 8. 0 6. 8 29. 0 12. 4 7. 3 26. 8 17. 9 8. 2 24. 4 24. 5 9. 0 22. 0 34. 5 9. 8 20. 5 43. 0 10. 3 19. 5 49. 0 10. 8 240 260 41. 9 4. 4 6. 0 34. 9 8. 0 6. 9 30. 5 12. 6 7. 5 28. 0 18. 0 8. 4 26. 0 25. 0 9. 2 23. 5 34. 5 10. 0 21. 8 44. 0 10. 6 20. 9 50. 5 11. 1 260 280 44. 5 4. 4 6. 2 36. 8 8. 0 7. 0 32. 4 12. 9 7. 8 29. 5 18. 0 8. 5 27. 7 25. 0 9. 4 25. 0 35. 0 10. 2 23. 0 45. 0 10. 9 22. 0 51. 5 11. 3 280 300 47. 0 4. 4 6. 3 38. 5 8. 0 7. 1 34. 1 13. 1 8. 0 31. 5 18. 0 8. 7 29. 0 25. 0 9. 5 26. 3 35. 0 10. 4 24. 3 45. 0 11. 1 23. 2 53. 0 11. 6 300 320 40. 5 8. 0 7. 2 36. 0 13. 3 8. 2 33. 0 18. 0 8. 9 30. 2 25. 0 9. 6 27. 6 35. 5 10. 6 25. 5 45. 5 11. 2 24. 5 54. 0 11. 8 320 340 42. 4 8. 0 7. 3 37. 6 13. 4 8. 3 34. 2 18. 0 9. 0 31. 6 25. 0 9. 8 29. 0 36. 0 10. 8 26. 7 46. 0 11. 4 25. 5 55. 0 12. 0 340 360 44. 2 8. 0 7. 4 38. 8 13. 4 8. 4 35. 7 18. 1 9. 1 33. 0 25. 0 9. 9 30. 0 36. 5 10. 9 27. 7 46. 5 11. 6 26. 6 55. 0 12. 2 360 380 46. 1 8. 0 7. 5 40. 2 13. 5 8. 5 37. 1 18. 2 9. 3 34. 2 25. 5 10. 0 31. 3 37. 0 11. 1 29. 1 47. 0 11. 8 27. 7 55. 5 12. 4 380 400 48. 0 8. 0 7. 7 42. 2 13. 5 8. 6 38. 8 18. 4 9. 5 35. 6 26. 0 10. 2 32. 5 37. 0 11. 2 30. 2 47. 5 12. 0 28. 9 56. 0 12. 6 400 420 50. 0 8. 0 7. 8 43. 5 13. 6 8. 7 40. 0 18. 7 9. 6 36. 9 26. 5 10. 3 33. 7 37. 5 11. 4 31. 5 47. 5 12. 2 29. 6 56. 5 12. 7 420 440 52. 0 8. 0 7. 9 44. 7 13. 7 8. 8 41. 3 18. 8 9. 7 38. 1 27. 0 10. 4 34. 8 37. 5 11. 5 32. 5 48. 0 12. 3 30. 9 57. 0 12. 9 440 460 54. 0 8. 0 8. 0 46. 2 13. 7 8. 9 42. 8 19. 0 9. 8 39. 5 27. 5 10. 6 36. 0 37. 5 11. 7 33. 5 48. 5 12. 5 31. 8 57. 5 13. 1 460 480 56. 0 8. 0 8. 1 47. 8 13. 7 9. 0 44. 0 19. 0 9. 9 41. 0 27. 5 10. 8 37. 0 37. 5 11. 8 34. 5 49. 0 12. 6 32. 7 57. 5 13. 2 480 500 58. 0 8. 0 8. 2 49. 2 13. 8 9. 1 45. 5 19. 1 10. 1 42. 1 27. 5 10. 9 38. 3 38. 0 11. 9 35. 5 49. 0 12. 7 33. 9 58. 0 13. 4 500 550 53. 0 13. 8 9. 3 48. 5 19. 5 10. 3 44. 9 27. 5 11. 1 41. 0 38. 5 12. 2 38. 2 50. 0 13. 0 36. 5 59. 0 13. 7 550 600 56. 3 13. 8 9. 5 51. 8 19. 7 10. 5 47. 7 27. 5 11. 3 43. 6 39. 0 12. 5 40. 3 50. 0 13. 3 38. 7 60. 0 14. 0 600 650 55. 0 19. 8 10. 7 50. 3 27. 5 11. 6 46. 4 39. 5 12. 8 43. 0 50. 0 13. 7 41. 0 60. 0 14. 2 650 700 58. 5 19. 8 11. 0 53. 2 27. 5 11. 8 49. 0 40. 0 13. 1 45. 4 50. 5 14. 0 43. 5 60. 5 14. 5 700 750 56. 2 27. 5 12. 1 51. 0 40. 0 13. 3 48. 0 51. 0 14. 2 45. 8 61. 0 14. 8 750 800 59. 2 27. 5 12. 3 53. 8 40. 0 13. 5 50. 6 51. 5 14. 5 47. 8 61. 5 15. 0 800 850 56. 2 40. 0 13. 8 52. 5 52. 0 14. 6 50. 0 62. 0 15. 2 850 900 58. 2 40. 0 14. 0 54. 6 52. 0 14. 9 52. 0 62. 5 15. 5 900 950 57. 2 52. 0 15. 1 54. 0 63.0 15. 7 950 1000 59. 3 52. 0 15. 3 56. 3 63. 0 16. 0 1000 Table 3202. Minimum Time (T) in hours that wind must blow to form waves of H significant height (in feet) and P period (in seconds). Fetch in nautical miles.
relationship in knots to the period (P) in seconds is given by the formula The relationship for sea is not known. The theoretical relationship between speed, wavelength, and period is shown in Figure 3202b. As waves continue on beyond the generating area, the period, wavelength, and speed remain the same. Because the waves of each period have different speeds they tend to sort themselves by periods as they move away from the generating area. The longer period waves move at a greater speed and move ahead. At great enough distances from a storm area the waves will have sorted themselves into sets based on period. All waves are attenuated as they propagate but the short period waves attenuate faster, so that far from a storm only the longer waves remain. The time needed for a wave system to travel a given distance is double that which would be indicated by the speed of individual waves. This is because each leading wave in succession gradually disappears and transfers its energy to following wave. The process occurs such that the whole wave system advances at a speed which is just half that of each individual wave. This process can easily be seen in the bow wave of a vessel. The speed at which the wave system advances is called group velocity. Because of the existence of many independent wave systems at the same time, the sea surface acquires a complex and irregular pattern. Since the longer waves overrun the shorter ones, the resulting interference adds to the complexity of the pattern. The process of interference, illustrated in Figure 3202c, is duplicated many times in the sea; it is the principal reason that successive waves are not of the same height. The irregularity of the surface may be further accentuated by the presence of wave systems crossing at an angle to each other, producing peak-like rises. Figure 3202b. Relationship between speed, length, and period of waves in deep water, based upon the theoretical relationship between period and length. S = 3.03P. Figure 3202c. Interference. The upper part of A shows two waves of equal height and nearly equal length traveling in the same direction. The lower part of A shows the resulting wave pattern. In B similar information is shown for short waves and long swell.
In reporting average wave heights, the mariner has a tendency to neglect the lower ones. It has been found that the reported value is about the average for the highest onethird. This is sometimes called the “significant” wave height. The approximate relationship between this height and others, is as follows:

### 3203. Path of Water Particles in a Wave

As shown in Figure 3203, a particle of water on the surface of the ocean follows a somewhat circular orbit as a wave passes, but moves very little in the direction of motion of the wave. The common wave producing this action is called an oscillatory wave. As the crest passes, the particle moves forward, giving the water the appearance of moving with the wave. As the trough passes, the motion is in the opposite direction. The radius of the circular orbit decreases with depth, approaching zero at a depth equal to about half the wavelength. In shallower water the orbits become more elliptical, and in very shallow water the vertical motion disappears almost completely. Since the speed is greater at the top of the orbit than at the bottom, the particle is not at exactly its original point following passage of a wave, but has moved slightly in the wave’s direction of motion. However, since this advance is small in relation to the vertical displacement, a floating object is raised and lowered by passage of a wave, but moved little from its original position. If this were not so, a slow moving vessel might experience considerable difficulty in making way against a wave train. In Figure 3203 the forward displacement is greatly exaggerated.

### 3204. Effects of Current and Ice on Waves

A following current increases wavelengths and decreases wave heights. An opposing current has the opposite effect, decreasing the length and increasing the height. This effect can be dangerous in certain areas of the world where a stream current opposes waves generated by severe weather. An example of this effect is off the coast of South Africa, where the Agulhas current is often opposed by westerly storms, creating steep, dangerous seas. A strong opposing current may cause the waves to break, as in the case of overfalls in tidal currents. The extent of wave alteration is dependent upon the ratio of the still-water wave speed to the speed of the current.
Moderate ocean currents running at oblique angles to wave directions appear to have little effect, but strong tidal currents perpendicular to a system of waves have been observed to completely destroy them in a short period of time.
When ice crystals form in seawater, internal friction is greatly increased. This results in smoothing of the sea surface. The effect of pack ice is even more pronounced. A vessel following a lead through such ice may be in smooth water even when a gale is blowing and heavy seas are beating against the outer edge of the pack. Hail or torrential rain is also effective in flattening the sea, even in a high wind.

### 3205. Waves and Shallow Water

When a wave encounters shallow water, the movement of the water is restricted by the bottom, resulting in reduced wave speed. In deep water wave speed is a function of period. In shallow water, the wave speed becomes a function of depth. The shallower the water, the slower the wave speed. As the wave speed slows, the period remains the same, so the wavelength becomes shorter. Since the energy in the waves remains the same, the shortening of wavelengths results in increased heights. This process is called shoaling. If the wave approaches a shallow area at an angle, each part is slowed successively as the depth decreases. This causes a change in direction of motion, or refraction, the wave tending to change direction parallel to the depth curves. The effect is similar to the refraction of light and other forms of radiant energy. As each wave slows, the next wave behind it, in deeper water, tends to catch up. As the wavelength decreases, the height generally becomes greater. The lower part of a wave, being nearest the bottom, is slowed more than the top. This may cause the wave to become unstable, the faster-moving top falling forward or breaking. Such a wave is called a breaker, and a series of breakers is surf. Swell passing over a shoal but not breaking undergoes a decrease in wavelength and speed, and an increase in height, which may be sudden and dramatic, depending on the steepness of the seafloor’s slope. This ground swell Wave Relative height Average 0.64 Significant 1.00 Highest 10 percent 1.29 Highest 1.87 Figure 3203. Orbital motion and displacement, s, of a particle on the surface of deep water during two wave periods.
may cause heavy rolling if it is on the beam and its period is the same as the period of roll of a vessel, even though the sea may appear relatively calm. It may also cause a rage sea, when the swell waves encounter water shoal enough to make them break. Rage seas are dangerous to small craft, particularly approaching from seaward, as the vessel can be overwhelmed by enormous breakers in perfectly calm weather. The swell waves, of course, may have been generated hundreds of miles away. In the open ocean they are almost unnoticed due to their very long period and wavelength. Figure 3205 illustrates the approximate alteration of the characteristics of waves as they cross a shoal.

### 3206. Energy Of Waves

The potential energy of a wave is related to the vertical distance of each particle from its still-water position. Therefore potential energy moves with the wave. In contrast, the kinetic energy of a wave is related to the speed of the particles, distributed evenly along the entire wave. The amount of kinetic energy in a wave is tremendous. A 4-foot, 10-second wave striking a coast expends more than 35,000 horsepower per mile of beach. For each 56 miles of coast, the energy expended equals the power generated at Hoover Dam. An increase in temperature of the water in the relatively narrow surf zone in which this energy is expended would seem to be indicated, but no pronounced increase has been measured. Apparently, any heat that may be generated is dissipated to the deeper water beyond the surf zone.

### 3207. Wave Measurement Aboard Ship

With suitable equipment and adequate training, reliable measurements of the height, length, period, and speed of waves can be made. However, the mariner’s estimates of height and length often contain relatively large errors. There is a tendency to underestimate the heights of low waves, and overestimate the heights of high ones. There are numerous accounts of waves 75 to 80 feet high, or even higher, although waves more than 55 feet high are very rare. Wavelength is usually underestimated. The motions of the vessel from which measurements are made contribute to such errors.
Height. Measurement of wave height is particularly difficult. A microbarograph can be used if the wave is long enough or the vessel small enough to permit the vessel to ride from crest to trough. If the waves are approaching from dead ahead or dead astern, this requires a wavelength at least twice the length of the vessel. For most accurate results the instrument should be placed at the center of roll and pitch, to minimize the effects of these motions. Wave height can often be estimated with reasonable accuracy by comparing it with freeboard of the vessel. This is less accurate as wave height and vessel motion increase. If a point of observation can be found at which the top of a wave is in line with the horizon when the observer is in the trough, the wave height is equal to height of eye. However, if the vessel is rolling or pitching, this height at the moment of observation may be difficult to determine. The highest wave ever reliably reported was 112 feet observed from the USS Ramapo in 1933.
Length. The dimensions of the vessel can be used to determine wavelength. Errors are introduced by perspective and disturbance of the wave pattern by the vessel. These errors are minimized if observations are made from maximum height. Best results are obtained if the sea is from dead ahead or dead astern.
Period. If allowance is made for the motion of the vessel, wave period can be determined by measuring the
Figure 3205. Alteration of the characteristics of waves crossing a shoal.
interval between passages of wave crests past the observer. The relative motion of the vessel can be eliminated by timing the passage of successive wave crests past a patch of foam or a floating object at some distance from the vessel. Accuracy of results can be improved by averaging several observations.
Speed. Speed can be determined by timing the passage of the wave between measured points along the side of the ship, if corrections are applied for the direction of travel for the wave and the speed of the ship.
The length, period, and speed of waves are interrelated by the relationships indicated previously. There is no definite mathematical relationship between wave height and length, period, or speed.

### 3208. Tsunamis

A Tsunami is an ocean wave produced by sudden, large-scale motion of a portion of the ocean floor or the shore, such as a volcanic eruption, earthquake (sometimes called seaquake if it occurs at sea), or landslide. If they are caused by a submarine earthquake, they are usually called seismic sea waves. The point directly above the disturbance, at which the waves originate, is called the epicenter. Either a tsunami or a storm tide that overflows the land is popularly called a tidal wave, although it bears no relation to the tide.
If a volcanic eruption occurs below the surface of the sea, the escaping gases cause a quantity of water to be pushed upward in the shape of a dome. The same effect is caused by the sudden rising of a portion of the bottom. As this water settles back, it creates a wave which travels at high speed across the surface of the ocean.
Tsunamis are a series of waves. Near the epicenter, the first wave may be the highest. At greater distances, the highest wave usually occurs later in the series, commonly between the third and the eighth wave. Following the maximum, they again become smaller, but the tsunami may be detectable for several days.
In deep water the wave height of a tsunami is probably never greater than 2 or 3 feet. Since the wavelength is usually considerably more than 100 miles, the wave is not conspicuous at sea. In the Pacific, where most tsunamis occur, the wave period varies between about 15 and 60 minutes, and the speed in deep water is more than 400 knots. The approximate speed can be computed by the formula: where S is the speed in knots, g is the acceleration due to gravity (32.2 feet per second per second), and d is the depth of water in feet. This formula is applicable to any wave in water having a depth of less than half the wavelength. For most ocean waves it applies only in shallow water, because of the relatively short wavelength.
When a tsunami enters shoal water, it undergoes the same changes as other waves. The formula indicates that speed is proportional to depth of water. Because of the great speed of a tsunami when it is in relatively deep water, the slowing is relatively much greater than that of an ordinary wave crested by wind. Therefore, the increase in height is also much greater. The size of the wave depends upon the nature and intensity of the disturbance. The height and destructiveness of the wave arriving at any place depends upon its distance from the epicenter, topography of the ocean floor, and the coastline. The angle at which the wave arrives, the shape of the coastline, and the topography along the coast and offshore, all have an effect. The position of the shore is also a factor, as it may be sheltered by intervening land, or be in a position where waves have a tendency to converge, either because of refraction or reflection, or both. Tsunamis 50 feet in height or higher have reached the shore, inflicting widespread damage. On April 1, 1946, seismic sea waves originating at an epicenter near the Aleutians spread over the entire Pacific. Scotch Cap Light on Unimak Island, 57 feet above sea level, was completely destroyed and its keepers killed. Traveling at an average speed of 490 miles per hour, the waves reached the Hawaiian Islands in 4 hours and 34 minutes, where they arrived as waves 50 feet above the high water level, and flooded a strip of coast more than 1,000 feet wide at some places. They left a death toll of 173 and property damage of $25 million. Less destructive waves reached the shores of North and South America, as well as Australia, 6,700 miles from the epicenter.
After this disaster, a tsunami warning system was set up in the Pacific, even though destructive waves are relatively rare (averaging about one in 20 years in the Hawaiian Islands). This system monitors seismic disturbances throughout the Pacific basin and predicts times and heights of tsunamis. Warnings are immediately sent out if a disturbance is detected. In addition to seismic sea waves, earthquakes below the surface of the sea may produce a longitudinal pressure wave that travels upward at the speed of sound. When a ship encounters such a wave, it is felt as a sudden shock which may be so severe that the crew thinks the vessel has struck bottom.

### 3209. Storm Tides

In relatively tideless seas like the Baltic and Mediterranean, winds cause the chief fluctuations in sea level. Elsewhere, the astronomical tide usually masks these variations. However, under exceptional conditions, either severe extra-tropical storms or tropical cyclones can produce changes in sea level that exceed the normal range of tide. Low sea level is of little concern except to coastal shipping, but a rise above ordinary high-water mark, particularly when it is accompanied by high waves, can result in a catastrophe.
Although, like tsunamis, these storm tides or storm surges are popularly called tidal waves, they are not associated with the tide. They consist of a single wave crest
S = 0.6 gd = 3.4 d
and hence have no period or wavelength.
Three effects in a storm induce a rise in sea level. The first is wind stress on the sea surface, which results in a piling-up of water (sometimes called “wind set-up”). The second effect is the convergence of wind-driven currents, which elevates the sea surface along the convergence line. In shallow water, bottom friction and the effects of local topography cause this elevation to persist and may even intensify it. The low atmospheric pressure that accompanies severe storms causes the third effect, which is sometimes referred to as the “inverted barometer” as the sea surface rises into the low pressure area. An inch of mercury is equivalent to about 13.6 inches of water, and the adjustment of the sea surface to the reduced pressure can amount to several feet at equilibrium.
All three of these causes act independently, and if they happen to occur simultaneously, their effects are additive. In addition, the wave can be intensified or amplified by the effects of local topography. Storm tides may reach heights of 20 feet or more, and it is estimated that they cause threefourths of the deaths attributed to hurricanes.

### 3210. Standing Waves and Seiches

Previous articles in this chapter have dealt with progressive waves which appear to move regularly with time. When two systems of progressive waves having the same period travel in opposite directions across the same area, a series of standing waves may form. These appear to remain stationary.
Another type of standing wave, called a seiche, sometimes occurs in a confined body of water. It is a long wave, usually having its crest at one end of the confined space, and its trough at the other. Its period may be anything from a few minutes to an hour or more, but somewhat less than the tidal period. Seiches are usually attributed to strong winds or sudden changes in atmospheric pressure.

### 3211. Tide-Generated Waves

There are, in general, two regions of high tide separated by two regions of low tide, and these regions move progressively westward around the Earth as the moon revolves in its orbit. The high tides are the crests of these tide waves, and the low tides are the troughs. The wave is not noticeable at sea, but becomes apparent along the coasts, particularly in funnelshaped estuaries. In certain river mouths, or estuaries of particular configuration, the incoming wave of high water overtakes the preceding low tide, resulting in a steep, breaking wave which progresses upstream in a surge called a bore.

### 3212. Internal Waves

Thus far, the discussion has been confined to waves on the surface of the sea, the boundary between air and water. Internal waves, or boundary waves, are created below the surface, at the boundaries between water strata of different densities. The density differences between adjacent water strata in the sea are considerably less than that between sea and air. Consequently, internal waves are much more easily formed than surface waves, and they are often much larger. The maximum height of wind waves on the surface is about 60 feet, but internal wave heights as great as 300 feet have been encountered.
Internal waves are detected by a number of observations of the vertical temperature distribution, using recording devices such as the bathythermograph. They have periods as short as a few minutes, and as long as 12 or 24 hours, these greater periods being associated with the tides. A slow-moving ship, operating in a freshwater layer having a depth approximating the draft of the vessel, may produce short-period internal waves. This may occur off rivers emptying into the sea, or in polar regions in the vicinity of melting ice. Under suitable conditions, the normal propulsion energy of the ship is expended in generating and maintaining these internal waves and the ship appears to “stick” in the water, becoming sluggish and making little headway. The phenomenon, known as dead water, disappears when speed is increased by a few knots. The full significance of internal waves has not yet been determined, but it is known that they may cause submarines to rise and fall like a ship at the surface, and they may also affect sound transmission in the sea.

### 3213. Waves and Ships

The effects of waves on a ship vary considerably with the type of ship, its course and speed, and the condition of the sea. A short vessel has a tendency to ride up one side of a wave and down the other side, while a larger vessel may tend to ride through the waves on an even keel. If the waves are of such length that the bow and stern of a vessel are alternately riding in successive crests and troughs, the vessel is subject to heavy sagging and hogging stresses, and under extreme conditions may break in two.A change of heading may reduce the danger. Because of the danger from sagging and hogging, a small vessel is sometimes better able to ride out a storm than a large one.
If successive waves strike the side of a vessel at the same phase of successive rolls, relatively small waves can cause heavy rolling. The same effect, if applied to the bow or stern in time with the natural period of pitch, can cause heavy pitching. A change of either heading or speed can quickly reduce the effect.
A wave having a length twice that of a ship places that ship in danger of falling off into the trough of the sea, particularly if it is a slow-moving vessel. The effect is especially pronounced if the sea is broad on the bow or broad on the quarter. An increase in speed reduces the hazard.

### 3214. Using Oil to Calm Breaking Waves

Historically oil was used to calm breaking waves, and was useful to vessels when lowering or hoisting boats in rough weather. Its effect was greatest in deep water, where a small quantity sufficed if the oil were made to spread to windward of the vessel. Oil increases the surface tension of the water, lessening the tendency for waves to break.

## BREAKERS AND SURF
### 3215. Refraction

As explained previously, waves are slowed in shallow water, causing refraction if the waves approach the beach at an angle. Along a perfectly straight beach, with uniform shoaling, the wave fronts tend to become parallel to the shore. Any irregularities in the coastline or bottom contours, however, affect the refraction, causing irregularities. In the case of a ridge perpendicular to the beach, for instance, the shoaling is more rapid, causing greater refraction towards the ridge. The waves tend to align themselves with the bottom contours. Waves on both sides of the ridge have a component of motion toward the ridge. This convergence of wave energy toward the ridge causes an increase in wave or breaker height. A submarine canyon or valley perpendicular to the beach, on the other hand, produces divergence, with a decrease in wave or breaker height. These effects are illustrated in Figure 3215. Bends in the coast line have a similar effect, convergence occurring at a point, and divergence if the coast is concave to the sea. Points act as focal areas for wave energy and experience large breakers. Concave bays have small breakers because the energy is spread out as the waves approach the beach.
Under suitable conditions, currents also cause refraction. This is of particular importance at entrances of tidal estuaries. When waves encounter a current running in the opposite direction, they become higher and shorter. This results in a choppy sea, often with breakers. When waves move in the same direction as current, they decrease in height, and become longer. Refraction occurs when waves encounter a current at an angle. Refraction diagrams, useful in planning amphibious operations, can be prepared with the aid of nautical charts or aerial photographs. When computer facilities are available, computer programs can be used to produce refraction diagrams quickly and accurately.

### 3216. Classes Of Breakers

In deep water, swell generally moves across the surface as somewhat regular, smooth undulations. When shoal water is reached, the wave period remains the same, but the speed decreases. The amount of decrease is negligible until the depth of water becomes about one-half the wavelength, when the waves begin to “feel” bottom. There is a slight decrease in wave height, followed by a rapid increase, if the waves are traveling perpendicular to a straight coast with a uniformly sloping bottom. As the waves become higher and shorter, they also become steeper, and the crest narrows. When the speed of the crest becomes greater than that of the wave, the front face of the wave becomes steeper than the rear face. This process continues at an accelerating rate as the depth of water decreases. If the wave becomes too unstable, it topples forward to form a breaker.
Figure 3215. The effect of bottom topography in causing wave convergence and wave divergence. Courtesy of Robert L. Wiegel, Council on Wave Research, University of California.
There are three general classes of breakers. A spilling breaker breaks gradually over a considerable distance. A plunging breaker tends to curl over and break with a single crash. A surging breaker peaks up, but surges up the beach without spilling or plunging. It is classed as a breaker even though it does not actually break. The type of breaker which forms is determined by the steepness of the beach and the steepness of the wave before it reaches shallow water, as illustrated in Figure 3216.
Long waves break in deeper water, and have a greater breaker height. A steep beach also increases breaker height. The height of breakers is less if the waves approach the beach at an acute angle. With a steeper beach slope there is greater tendency of the breakers to plunge or surge. Following the uprush of water onto a beach after the breaking of a wave, the seaward backrush occurs. The returning water is called backwash. It tends to further slow the bottom of a wave, thus increasing its tendency to break. This effect is greater as either the speed or depth of the backwash increases. The still water depth at the point of breaking is approximately 1.3 times the average breaker height.
Surf varies with both position along the beach and time. A change in position often means a change in bottom contour, with the refraction effects discussed before. At the same point, the height and period of waves vary consid-
Figure 3216. The three types of breakers. Courtesy of Robert L. Wiegel, Council on Wave Research, University of California.
erably from wave to wave. A group of high waves is usually followed by several lower ones. Therefore, passage through surf can usually be made most easily immediately following a series of higher waves. Since surf conditions are directly related to height of the waves approaching a beach, and to the configuration of the bottom, the state of the surf at any time can be predicted if one has the necessary information and knowledge of the principles involved. Height of the sea and swell can be predicted from wind data, and information on bottom configuration can sometimes be obtained from the largest scale nautical chart. In addition, the area of lightest surf along a beach can be predicted if details of the bottom configuration are available. Surf predictions may, however, be significantly in error due to the presence of swell from unknown storms hundreds of miles away.

### 3217. Currents in the Surf Zone

In and adjacent to the surf zone, currents are generated by waves approaching the bottom contours at an angle, and by irregularities in the bottom. Waves approaching at an angle produce a longshore current parallel to the beach, inside of the surf zone. Longshore currents are most common along straight beaches. Their speeds increase with increasing breaker height, decreasing wave period, increasing angle of breaker line with the beach, and increasing beach slope. Speed seldom exceeds 1 knot, but sustained speeds as high as 3 knots have been recorded. Longshore currents are usually constant in direction. They increase the danger of landing craft broaching to.
Where the bottom is sandy a good distance offshore, one or more sand bars typically form. The innermost bar will break in even small waves, and will isolate the longshore current. The second bar, if one forms, will break only in heavier weather, and the third, if present, only in storms. It is possible to move parallel to the coast in small craft in relatively deep water in the area between these bars, between the lines of breakers.

### 3218. Rip Currents

As explained previously, wave fronts advancing over nonparallel bottom contours are refracted to cause convergence or divergence of the energy of the waves. Energy concentrations in areas of convergence form barriers to the returning backwash, which is deflected along the beach to areas of less resistance. Backwash accumulates at weak points, and returns seaward in concentrations, forming rip currents through the surf. At these points the large volume of returning water has an easily seen retarding effect upon the incoming waves, thus adding to the condition causing the rip current. The waves on one or both sides of the rip, having greater energy and not being retarded by the concentration of backwash, advance faster and farther up the beach. From here, they move along the beach as feeder currents. At some point of low resistance, the water flows seaward through the surf, forming the neck of the rip current. Outside the breaker line the current widens and slackens, forming the head. The various parts of a rip current are shown in Figure 3218.
Rip currents may also be caused by irregularities in the beach face. If a beach indentation causes an uprush to advance farther than the average, the backrush is delayed and this in turn retards the next incoming foam line (the front of a wave as it advances shoreward after breaking) at that point. The foam line on each side of the retarded point continues in its advance, however, and tends to fill in the retarded area, producing a rip current.
Rip currents are dangerous for swimmers, but may provide a clear path to the beach for small craft, as they tend to scour out the bottom and break through any sand bars that have formed. Rip currents also change location over time as conditions change.
Figure 3218. A rip current (left) and a diagram of its parts (right). Courtesy of Robert L. Wiegel, Council on Wave Research, University of California.

### 3219. Beach Sediments

In the surf zone, large amounts of sediment are suspended in the water. When the water’s motion decreases, the sediments settle to the bottom. The water motion can be either waves or currents. Promontories or points are rocky because the large breakers scour the points and small sediments are suspended in the water and carried away. Bays tend to have sandy beaches because of the smaller waves.
In the winter when storms create large breakers and surf, the waves erode beaches and carry the particles offshore where offshore sand bars form; sandy beaches tend to be narrower in stormy seasons. In the summer the waves gradually move the sand back to the beaches and the offshore sand bars decrease; then sandy beaches tend to be wider.
Longshore currents move large amounts of sand along the coast. These currents deposit sand on the upcurrent side of a jetty or pier, and erode the beach on the downcurrent side. Groins are sometimes built to impede the longshore flow of sediments and preserve beaches for recreational use. As with jetties, the downcurrent side of each groin will have the best water for approaching the beach.