IPR2017-00946
`Garmin EX2001 Page 451
`
`IPR2017-00946
`Garmin EX2001 Page 451
`
`

`

`CHAPTER 32
`
`WAVES, BREAKERS AND SURF
`
`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 instanta-
`neously. 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
`proventhemodeltobeverygood.Informationfromthemodel
`is provided to the U.S. Navy on a routine basis and is a vital
`input to the Optimum Track Ship Routing program.
`
`OCEAN WAVES
`3202. Wave Characteristics
`Ocean waves are very nearly in the shape of an in-
`verted 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 dis-
`tance between trough and crest is called wave height,
`labeled H in Figure 3202a. The horizontal distance be-
`tween 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.
`
`Figure 3202a. A typical sea wave.
`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:
`5.12 P2.
`L
`=
`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 generat-
`ing 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
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`442
`
`WAVES, BREAKERS AND SURF
`
`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.
`
`59. 352. 015. 356. 363. 016. 01000
`57. 252. 015. 154. 063.015. 7950
`58. 240. 014. 054. 652. 014. 952. 062. 515. 5900
`56. 240. 013. 852. 552. 014. 650. 062. 015. 2850
`59. 227. 512. 353. 840. 013. 550. 651. 514. 547. 861. 515. 0800
`56. 227. 512. 151. 040. 013. 348. 051. 014. 245. 861. 014. 8750
`58. 519. 811. 053. 227. 511. 849. 040. 013. 145. 450. 514. 043. 560. 514. 5700
`55. 019. 810. 750. 327. 511. 646. 439. 512. 843. 050. 013. 741. 060. 014. 2650
`9. 551. 819. 710. 547. 727. 511. 343. 639. 012. 540. 350. 013. 338. 760. 014. 0600
`9. 348. 519. 510. 344. 927. 511. 141. 038. 512. 238. 250. 013. 036. 559. 013. 7550
`9. 145. 519. 110. 142. 127. 510. 938. 338. 011. 935. 549. 012. 733. 958. 013. 4500
`9. 941. 027. 510. 837. 037. 511. 834. 549. 012. 632. 757. 513. 2480
`9. 044. 019. 0
`9. 839. 527. 510. 636. 037. 511. 733. 548. 512. 531. 857. 513. 1460
`8. 942. 819. 0
`9. 738. 127. 010. 434. 837. 511. 532. 548. 012. 330. 957. 012. 9440
`8. 841. 318. 8
`9. 636. 926. 510. 333. 737. 511. 431. 547. 512. 229. 656. 512. 7420
`8. 740. 018. 7
`9. 535. 626. 010. 232. 537. 011. 230. 247. 512. 028. 956. 012. 6400
`8. 638. 818. 4
`9. 334. 225. 510. 031. 337. 011. 129. 147. 011. 827. 755. 512. 4380
`8. 537. 118. 2
`9. 930. 036. 510. 927. 746. 511. 626. 655. 012. 2360
`9. 133. 025. 0
`8. 435. 718. 1
`9. 829. 036. 010. 826. 746. 011. 425. 555. 012. 0340
`9. 031. 625. 0
`8. 334. 218. 0
`9. 627. 635. 510. 625. 545. 511. 224. 554. 011. 8320
`8. 930. 225. 0
`8. 233. 018. 0
`9. 526. 335. 010. 424. 345. 011. 123. 253. 011. 6300
`8. 729. 025. 0
`8. 031. 518. 0
`9. 425. 035. 010. 223. 045. 010. 922. 051. 511. 3280
`8. 527. 725. 0
`7. 829. 518. 0
`9. 223. 534. 510. 021. 844. 010. 620. 950. 511. 1260
`8. 426. 025. 0
`7. 528. 018. 0
`9. 820. 543. 010. 319. 549. 010. 8240
`9. 022. 034. 5
`8. 224. 424. 5
`7. 326. 817. 9
`9. 619. 141. 510. 118. 247. 510. 6220
`8. 820. 934. 0
`8. 022. 924. 0
`7. 225. 017. 9
`9. 817. 146. 010. 3200
`9. 218. 140. 0
`8. 519. 332. 5
`7. 721. 523. 5
`7. 123. 117. 5
`9. 516. 044. 510. 0180
`9. 016. 538. 5
`8. 318. 031. 5
`7. 519. 923. 5
`6. 821. 317. 0
`9. 6160
`9. 114. 542. 5
`8. 715. 137. 0
`8. 016. 430. 5
`7. 318. 023. 0
`6. 619. 516. 5
`9. 2140
`8. 813. 040. 0
`8. 313. 935. 5
`7. 614. 829. 0
`7. 016. 022. 0
`6. 417. 616. 2
`8. 8120
`8. 411. 537. 5
`7. 912. 333. 5
`7. 313. 127. 5
`6. 714. 521. 5
`6. 215. 916. 0
`8. 5100
`8. 110. 335. 0
`7. 611. 032. 0
`6. 911. 926. 5
`6. 512. 820. 5
`6. 014. 015. 5
`90
`8. 2
`9. 534. 0
`7. 9
`7. 210. 230. 0
`6. 711. 025. 0
`6. 312. 020. 0
`5. 813. 015. 0
`80
`7. 9
`8. 631. 5
`7. 7
`9. 328. 0
`7. 1
`6. 610. 024. 0
`6. 011. 018. 9
`5. 612. 014. 5
`70
`7. 7
`7. 829. 5
`7. 3
`8. 326. 5
`6. 8
`9. 022. 5
`6. 4
`9. 918. 0
`5. 7
`5. 410. 513. 9
`60
`7. 5
`7. 027. 5
`7. 0
`7. 425. 0
`6. 5
`8. 021. 0
`6. 0
`8. 717. 0
`5. 5
`9. 613. 2
`5. 1
`50
`7. 1
`6. 125. 0
`6. 7
`6. 423. 0
`6. 3
`6. 919. 8
`5. 6
`7. 715. 7
`5. 2
`8. 412. 2
`4. 8
`40
`6. 7
`5. 122. 5
`6. 3
`5. 421. 0
`5. 9
`5. 817. 7
`5. 4
`6. 514. 0
`4. 9
`7. 111. 2
`4. 6
`30
`6. 3
`4. 119. 8
`6. 0
`4. 418. 0
`5. 5
`4. 715. 8
`5. 0
`5. 212. 1
`4. 6
`5. 810. 0
`4. 2
`20
`5. 9
`3. 016. 0
`5. 2
`3. 214. 0
`5. 0
`3. 512. 0
`4. 4
`3. 910. 0
`4. 3
`8. 6
`4. 2
`3. 8
`10
`5. 0
`1. 810. 0
`4. 2
`1. 910. 0
`4. 1
`8. 0
`2. 0
`3. 9
`7. 3
`2. 3
`3. 4
`6. 0
`2. 5
`3. 1
`
`56. 313. 8
`53. 013. 8
`8. 249. 213. 8
`8. 147. 813. 7
`8. 046. 213. 7
`7. 944. 713. 7
`7. 843. 513. 6
`7. 742. 213. 5
`7. 540. 213. 5
`7. 438. 813. 4
`7. 337. 613. 4
`7. 236. 013. 3
`7. 134. 113. 1
`7. 032. 412. 9
`6. 930. 512. 6
`6. 829. 012. 4
`6. 627. 212. 3
`6. 425. 412. 2
`6. 223. 112. 1
`6. 021. 112. 0
`5. 819. 111. 9
`5. 417. 011. 7
`5. 315. 111. 4
`5. 114. 111. 2
`4. 913. 011. 0
`4. 811. 910. 8
`4. 610. 210. 3
`9. 8
`4. 4
`9. 0
`4. 1
`8. 0
`3. 7
`7. 0
`3. 3
`5. 0
`2. 8
`
`9. 1
`7. 8
`6. 2
`4. 7
`2. 7
`
`Fetch
`
`P
`
`H
`
`11
`
`T
`
`P
`
`H
`
`10
`
`T
`
`P
`
`9
`
`H
`
`T
`
`P
`
`8
`
`H
`
`T
`
`P
`
`7
`
`H
`
`T
`
`P
`
`6
`
`H
`
`T
`
`P
`
`BEAUFORT NUMBER
`
`8. 0
`8. 0
`8. 0
`8. 0
`8. 0
`8. 0
`8. 0
`8. 0
`8. 0
`8. 0
`8. 0
`8. 0
`8. 0
`8. 0
`8. 0
`8. 0
`8. 0
`7. 9
`7. 9
`7. 8
`7. 3
`7. 3
`7. 2
`7. 0
`6. 8
`6. 5
`6. 2
`5. 8
`4. 9
`3. 5
`
`5
`
`H
`
`58. 0
`56. 0
`54. 0
`52. 0
`50. 0
`48. 0
`46. 1
`44. 2
`42. 4
`40. 5
`6. 338. 5
`6. 236. 8
`6. 034. 9
`5. 933. 1
`5. 831. 1
`5. 629. 0
`5. 427. 0
`5. 224. 3
`4. 922. 5
`4. 720. 0
`4. 417. 5
`4. 316. 5
`4. 215. 0
`4. 113. 5
`4. 012. 0
`3. 811. 0
`8. 9
`3. 6
`7. 2
`3. 3
`5. 4
`2. 9
`3. 2
`2. 4
`
`T
`
`P
`
`4. 4
`4. 4
`4. 4
`4. 4
`4. 4
`4. 3
`4. 3
`4. 2
`4. 2
`4. 1
`4. 0
`4. 0
`4. 0
`4. 0
`4. 0
`4. 0
`3. 9
`3. 8
`3. 2
`2. 6
`
`4
`
`H
`
`47. 0
`44. 5
`41. 9
`39. 2
`36. 5
`33. 5
`4. 930. 9
`4. 928. 4
`4. 525. 8
`4. 222. 4
`4. 020. 0
`3. 918. 8
`3. 817. 0
`3. 715. 8
`3. 514. 0
`3. 212. 4
`3. 010. 3
`8. 3
`2. 8
`6. 2
`2. 5
`3. 7
`2. 1
`
`T
`
`P
`
`2. 0
`2. 0
`2. 0
`2. 0
`2. 0
`2. 0
`2. 0
`2. 0
`2. 0
`2. 0
`2. 0
`2. 0
`2. 0
`1. 8
`
`3
`
`H
`
`1000
`950
`900
`850
`800
`750
`700
`650
`600
`550
`500
`480
`460
`440
`420
`400
`380
`360
`340
`320
`300
`280
`260
`240
`220
`200
`18050. 0
`16043. 2
`14036. 6
`12031. 1
`10027. 1
`9023. 6
`8020. 0
`7018. 0
`6016. 0
`5014. 0
`4012. 0
`9. 8
`30
`7. 1
`20
`4. 4
`10
`
`T
`
`Fetch
`
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`

`WAVES, BREAKERS AND SURF
`
`443
`
`Figure 3202b. Relationship between speed, length, and period of waves in deep water, based upon the theoretical
`relationship between period and length.
`relationship in knots to the period (P) in seconds is given by
`the formula
`3.03P.
`S
`=
`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 pe-
`riod waves move at a greater speed and move ahead. At great
`enough distances from a storm area the waves will have sort-
`ed 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
`
`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.
`the sea surface acquires a
`systems at
`the same time,
`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.
`
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`

`444
`
`WAVES, BREAKERS AND SURF
`
`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 one-
`third. This is sometimes called the “significant” wave
`height. The approximate relationship between this height
`and others, is as follows:
`Relative height
`Wave
`0.64
`Average
`1.00
`Significant
`1.29
`Highest 10 percent
`Highest
`1.87
`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.
`
`Figure 3203. Orbital motion and displacement, s, of a
`particle on the surface of deep water during two wave
`periods.
`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
`
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`WAVES, BREAKERS AND SURF
`
`445
`
`Figure 3205. Alteration of the characteristics of waves crossing a shoal.
`may cause heavy rolling if it is on the beam and its period
`speed of waves can be made. However, the mariner’s
`is the same as the period of roll of a vessel, even though the
`estimates of height and length often contain relatively large
`sea may appear relatively calm. It may also cause a rage
`errors. There is a tendency to underestimate the heights of
`sea, when the swell waves encounter water shoal enough to
`low waves, and overestimate the heights of high ones.
`make them break. Rage seas are dangerous to small craft,
`There are numerous accounts of waves 75 to 80 feet high,
`particularly approaching from seaward, as the vessel can be
`or even higher, although waves more than 55 feet high are
`overwhelmed by enormous breakers in perfectly calm
`very rare. Wavelength is usually underestimated. The
`weather. The swell waves, of course, may have been
`motions of the vessel from which measurements are made
`generated hundreds of miles away. In the open ocean they
`contribute to such errors.
`are almost unnoticed due to their very long period and
`Height. Measurement of wave height is particularly
`wavelength. Figure 3205 illustrates
`the approximate
`difficult. A microbarograph can be used if the wave is long
`alteration of the characteristics of waves as they cross a
`enough or the vessel small enough to permit the vessel to
`shoal.
`ride from crest to trough. If the waves are approaching from
`dead ahead or dead astern, this requires a wavelength at
`3206. Energy Of Waves
`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
`The potential energy of a wave is related to the vertical
`height can often be estimated with reasonable accuracy by
`distance of each particle from its still-water position. Therefore
`comparing it with freeboard of the vessel. This is less
`potential energy moves with the wave. In contrast, the kinetic
`accurate as wave height and vessel motion increase. If a
`energy of a wave is related to the speed of the particles,
`point of observation can be found at which the top of a wave
`distributed evenly along the entire wave.
`is in line with the horizon when the observer is in the
`The amount of kinetic energy in a wave is tremendous. A
`trough, the wave height is equal to height of eye. However,
`4-foot, 10-second wave striking a coast expends more than
`if the vessel is rolling or pitching, this height at the moment
`35,000 horsepower per mile of beach. For each 56 miles of
`of observation may be difficult to determine. The highest
`coast, the energy expended equals the power generated at
`wave ever reliably reported was 112 feet observed from the
`Hoover Dam. An increase in temperature of the water in the
`USS Ramapo in 1933.
`relatively narrow surf zone in which this energy is expended
`would seem to be indicated, but no pronounced increase has
`Length. The dimensions of the vessel can be used to
`been measured. Apparently, any heat that may be generated is
`determine wavelength. Errors are introduced by perspective
`dissipated to the deeper water beyond the surf zone.
`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
`3207. Wave Measurement Aboard Ship
`dead ahead or dead astern.
`Period. If allowance is made for the motion of the
`With suitable equipment and adequate training,
`vessel, wave period can be determined by measuring the
`reliable measurements of the height, length, period, and
`
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`446
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`WAVES, BREAKERS AND SURF
`
`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:
`S
`=
`0.6 gd
`=
`3.4 d
`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 Mediter-
`ranean, 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, partic-
`ularly 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
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`447
`
`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.
`Aninchofmercuryisequivalenttoabout13.6inchesofwater,
`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 three-
`fourths 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 progres-
`sively 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 funnel-
`shaped 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
`Thusfar,thediscussionhasbeenconfinedtowavesonthe
`surfaceofthesea,theboundarybetweenairandwater.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
`maybreakintwo.Achangeofheadingmayreducethedanger.
`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, partic-
`ularly 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
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`WAVES, BREAKERS AND SURF
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`windward of the vessel. Oil increases the surface tension of
`rough weather. Its effect was greatest in deep water, where
`the water, lessening the tendency for waves to break.
`a small quantity sufficed if the oil were made to spread to
`BREAKERS AND SURF
`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 avail-
`able, 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 wa-
`ter 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 de-
`crease 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