《航海学》课程参考文献（地文资料）CHAPTER 33 WAVES, BREAKERS AND SURF

CHAPTER33WAVES.BREAKERSANDSUREOCEANWAVES3300.Introduction3302.WaveCharacteristicsOcean Waves arethemost widelyobservedphenome-Ocean waves are very nearly in the shape of an invert-non at sea,and possiblytheleast understood bytheaverageed cycloid, the figure formed by a point inside the rim ofaseaman.Morethananyothersinglefactor.oceanwavesarewheel rolling along a level surface.This shape is shown inlikely to cause a navigator to change course or speed toFigure3302a.Thehighestparts of waves arecalled crestsavoid damageto ship and cargo.Wind-generated oceanand the intervening lowest parts, troughs.Since the crestswaves have been measured at more than 100feet high, andare steeperand narrower than the troughs, the mean or stilltsunamis, caused by earthquakes, far higher.A marinerwater level is a little lower than halfwaybetween the crestswithknowledgeof basic facts concerning waves is abletoand troughs.The vertical distancebetween trough and crestusethem to hisadvantage,avoid hazardous conditions,andis called wave height, labeled H in Figure3302a.The hor-operatewithaminimumofdangerif suchconditionscan-izontal distancebetween successivecrests,measured inthenot be avoided. See Chapter 38, Weather Routing, fordirection of travel, is called wavelength, labeled L.Thedetails on howto avoid areas of severe waves.time interval between passage of successive crests ata sta-tionary point is called wave period (P). Wave height,3301.CausesOfWaveslength,andperiod depend upon anumberoffactors,suchas thewind speed,thelength oftime it has blown, and itsWaves on the surface ofthe sea are caused principallyfetch (the straight distance it has traveled over the surface)by wind, but other factors, such as submarine earthquakes,Table 3302 indicates the relationshipbetween wind speed.volcanic eruptions, and the tide, also cause waves.If afetch,lengthoftimethewindblows,waveheight,andwavebreezeof lessthan2knotsstartstoblowacrosssmoothwa-period in deep water.ter,smallwaveletscalledripplesformalmostinstantaneously.When the breeze dies, the ripples disap-pear as suddenly as they formed, the level surface beingrestored by surface tension of the water.If thewind speedexceeds2knots,more stablegravitywavesgraduallyform,and progress withthewind.While thegenerating wind blows, the resulting wavesmay be referred to as sea.When the wind stops or changesSTILLWATERLEVELdirection.wavesthatcontinueonwithoutrelationtolocalwinds are called swell.Unlike wind and current, waves are not deflected ap-Figure 3302a. A typical sea wave.preciably by the rotation of the earth, but move in thedirection in whichthegeneratingwindblows.WhenthisIf thewater is deeperthan one-half the wavelength (L)wind ceases,friction and spreading cause the waves to bethis length in feet is theoretically related to period (P) inreduced in height, or attenuated, as they move.However.seconds by the formula:the reduction takes place so slowly that swell often contin-uesuntilitreachessomeobstruction,suchasashoreL = 5.12 p2TheFleet Numerical Meteorology and OceanographyCenterproduces synopticanalysesandpredictionsofoceanThe actual value has been found to be a little less thanwave heights using a spectral numerical model.The wavethis for swell, and about two-thirds the length determinedinformationconsistsofheightsanddirectionsfordifferentby this formulafor sea.When the waves leave the generat-periods and wavelengths.Verification of projected data hasproventhemodeltobeverygood.Informationfromtheing area and continue as freewaves,the wavelength andmodel is provided to the U.S.Navy on a routine basis and isperiodcontinue to increase, whiletheheight decreases.Theavital inputtotheOptimumTrackShipRoutingprogram.rateofchangegraduallydecreases.443

443 CHAPTER 33 WAVES, BREAKERS AND SURF OCEAN WAVES 3300. Introduction Ocean Waves are the most widely observed phenome￾non at sea, and possibly 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 can￾not be avoided. See Chapter 38, Weather Routing, for details on how to avoid areas of severe waves. 3301. 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 wa￾ter, small wavelets called ripples form almost instantaneously. When the breeze dies, the ripples disap￾pear 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 ap￾preciably 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 contin￾ues 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. 3302. Wave Characteristics Ocean waves are very nearly in the shape of an invert￾ed cycloid, the figure formed by a point inside the rim of a wheel rolling along a level surface. This shape is shown in Figure 3302a. 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 3302a. The hor￾izontal 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 sta￾tionary 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 3302 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 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. Figure 3302a. A typical sea wave. L 5.12 P2 =

Pa8.218.81313.015.011.034.01020.0415.20.511.9035.0e100851202.04. 2227.86..14.32127.7.933.3X.411.312012.39388806666125881800204.322235.514014036.625.8511917.616.2014.813.913.092040.07N星星房宾强43.28823nni19.160O1615.44150423259.44017. 095&18.06850.0215"10.0633.21.O232319Oo17.120041.546.R3634239.6222088008双332a欢欢欢验i2i2o17.N559.0488010E204845.4499.10.010.28.18.00082550Q525.53004544.312.729..007o.2010.28018.400*3a47.0213118.2500K2230048.07.230.22710.6区0玖观#板板板机3201333.0P09.6o11.18..5298.0319.8134013213.o034..60.0418.55124板888013.9635.90930.O110360218.6055.121328.37.18.a2510.0.3113800122842647a2.512.40010.28.38.N宇军多多家家目5强现4042026.R38V41033R83区区区55510烈强玖汉科44ini30.9星学0o6o618.990-45双儿卫.05019.5552610.1.849944.O012.19.8.213010495004512T3.84455050欢欢机机4310.19,61338.C013.825173455.010.41.19.n0ot酒洗544473019.142058..3602O08500BN区200056de15n95063.0550100052Table 3302. Minimum Time (T) in hours that wind must blow to form waves of H significant height (in feet) and P period (in secconds). Fetch in nautical miles

4 4 4 W A V E S , B R E A K E R S AN D S U R F 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 3302. Minimum Time (T) in hours that wind must blow to form waves of H significant height (in feet) and P period (in secconds). Fetch in nautical miles

445WAVES,BREAKERSANDSURFThe speed(S)ofa free wave in deep water is nearly independent of its height or steepness.For swell, itsrelationship in knots to the period (P) in seconds is given bytheformulaS = 3.03P ,The relationshipfor sea is not known.AAAThe theoretical relationship between speed, wavelength,and period is shown inFigure 3302b.As waves continue onbeyond the generating area, the period, wavelength,andAAAspeed remain the same. Because the waves of each periodhavedifferent speeds they tend to sort themselves byperiodsas they move away from the generating area.The longer pe-riod waves move ata greater speed and moveahead.Atgreatenoughdistancesfroma storm areathewaveswill havesortedthemselves intosetsbasedonperiodFigure 3302c.Interference.The upper part of A shows twowavesofequal heightandnearlyequal lengthtravelinginAll waves are attenuated as they propagate but thethe same direction.The lower part of A shows the resultingshortperiodwaves attenuatefaster,so thatfarfroma stormwavepatterm.InBsimilarinformationisshownforshortonly the longer waves remain.waves and long swell.Thetimeneededfora wavesystemtotravel agivendistance isdoublethatwhichwould beindicatedbytheBecause of the existence of manyindependent wavespeed of individual waves. This is because each leadingsystems at the same time, the sea surface acquires a com-wave in succession gradually disappears and transfers itsplex and irregular pattern. Since the longer waves overrunenergytofollowingwave.Theprocessoccurs suchthatthethe shorter ones, the resulting interference adds to the com-wholewavesystem advances at a speed which is just halfplexity of the pattern.The process of interference,that of each individual wave.This process can easily beillustrated inFigure 3302c,is duplicated many times in theseen in thebow wave of a vessel.The speed at which thewave system advances is called group velocitysea, it is the principal reason that successive waves are noteSOSELENGTH (LLFEETFigure3302b.Relationshipbetween speed, length,andperiodofwaves in deep water,basedupon thetheoreticalrelationshipbetweenperiod and length

WAVES, BREAKERS AND SURF 445 The speed (S) of a free wave in deep water is nearly in￾dependent of its height or steepness. For swell, its 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 3302b. 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 systems at the same time, the sea surface acquires a com￾plex and irregular pattern. Since the longer waves overrun the shorter ones, the resulting interference adds to the com￾plexity of the pattern. The process of interference, illustrated in Figure 3302c, is duplicated many times in the sea; it is the principal reason that successive waves are not S 3.03P . = Figure 3302c. 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. Figure 3302b. Relationship between speed, length, and period of waves in deep water, based upon the theoretical relationship between period and length

446WAVES,BREAKERSANDSURFlittle from its original position.If this were not so,a slowof thesameheight.Theirregularityofthe surfacemaybemovingvesselmightexperienceconsiderabledifficultyinfurtheraccentuatedbythepresenceofwavesystemscross-making way against a wave train.In Figure3303 thefor-ing at an angleto each other,producing peak-like rises.ward displacement is greatly exaggerated.In reporting average wave heights, the mariner has atenencytoneglect the lower ones.It has been found that the3304.EffectsOfCurrentsOnWavesreported value is about the average for the highest one-third. This is sometimes called the“significant"waveAfollowing current increases wavelengths and de-height. The approximate relationship between this heightcreases waveheights.An opposing current has the oppositeand others, is asfollows.effect, decreasing the lengthand increasing the height.Thiseffectcanbe dangerous in certain areas ofthe world whereWaveRelative heighta streamcurrentopposes wavesgeneratedby severeweath-er.An example of this effect is off the Coast of South0.64AverageAfrica,wheretheAgulhas currentis oftenopposedbywest-1.00Significanterly storms, creating steep,dangerous seas.A strong1.29Highest10percentopposing current may cause the waves to break,as in the1.87Highestcaseofoverfallsintidalcurrents.Theextentofwavealter-ation is dependent upon the ratio of the still-water wave3303.PathOfWaterParticlesInAWavespeed to the speed ofthe current.Moderate ocean currents running at obliqueanglestoAsshowninFigure3303,aparticleofwateron thesur-wavedirections appear to have littleeffect, but strong tidalcurrentsperpendiculartoasystemof waveshavebeenob-faceof theoceanfollowsa somewhatcircularorbitasaservedto completelydestroythem in a shortperiod oftimewavepasses,butmovesverylittleinthedirectionofmotionof the wave.Thecommon waveproducing thisaction is3305.TheEffectOf IceOnWavescalled an oscillatory wave. As the crest passes, the particlemovesforward,givingthewatertheappearanceofmovingWhen ice crystalsform in seawater,internal friction iswith the wave.As the troughpasses,themotion is intheop-greatly increased.This results in smoothing of the sea sur-posite direction.The radius of the circular orbit decreasesface.Theeffect of pack ice is even more pronounced.Awith depth, approaching zero at a depth equal to about halfvesselfollowinga lead through such icemaybein smooththewavelength.In shallower waterthe orbits becomemorewater even when agale is blowing and heavy seas are beat-elliptical, and in very shallow water thevertical motion dis-ing against the outer edge of thepack.Hail or torrential rainappearsalmostcompletely.is also effective in flattening the sea,even in a high wind.Since the speed is greater at the top of the orbit than atthe bottom, the particle is not at exactly its original point3306.WavesAndShallowWaterfollowing passageofa wave,buthas moved slightly in thewave's direction ofmotion.However,sincethis advance isWhen a wave encounters shallow water.themove-smallinrelationtotheverticaldisplacement,afloatingob-mentof the water is restricted bythe bottom,resulting inject is raised and lowered by passage of a wave,but movedreduced wave speed. In deep water wave speed is a func-tion of period.In shallow water,the wave speed becomesa function of depth.The shallower thewater,the slowerthe wave speed.As the wave speed slows, the period re-mains the same, so the wavelength becomes shorter.Since the energy in the waves remains the same, theshortening of wavelengths results in increased heights.This process is called shoaling.If the wave approachesa shallow area at an angle, each part is slowed succes-sively as the depth decreases. This causes a change indirection of motion, or refraction,thewavetendingtochange direction parallel to the depth curves.The effectis similartotherefraction of lightandotherforms ofra-diantenergyAs each wave slows, the next wave behind it, in deeperwater, tends to catch up. As the wavelength decreases, theFigure3303.Orbital motion and displacement,s,ofaheightgenerallybecomesgreater.The lower part ofawaveparticle on thesurfaceofdeepwaterduringtwowavebeing nearest the bottom, is slowed more than thetop.Thisperiods.may cause the wave tobecome unstable,the faster-moving

446 WAVES, BREAKERS AND SURF of the same height. The irregularity of the surface may be further accentuated by the presence of wave systems cross￾ing at an angle to each other, producing peak-like rises. In reporting average wave heights, the mariner has a tenency 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. 3303. Path Of Water Particles In A Wave As shown in Figure 3303, a particle of water on the sur￾face 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 op￾posite 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 dis￾appears 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 ob￾ject 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 3303 the for￾ward displacement is greatly exaggerated. 3304. Effects Of Currents On Waves A following current increases wavelengths and de￾creases 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 weath￾er. An example of this effect is off the Coast of South Africa, where the Agulhas current is often opposed by west￾erly 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 alter￾ation 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 ob￾served to completely destroy them in a short period of time. 3305. The Effect Of Ice On Waves When ice crystals form in seawater, internal friction is greatly increased. This results in smoothing of the sea sur￾face. 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 beat￾ing against the outer edge of the pack. Hail or torrential rain is also effective in flattening the sea, even in a high wind. 3306. Waves And Shallow Water When a wave encounters shallow water, the move￾ment of the water is restricted by the bottom, resulting in reduced wave speed. In deep water wave speed is a func￾tion 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 re￾mains 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 succes￾sively 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 ra￾diant 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 Wave Relative height Average 0.64 Significant 1.00 Highest 10 percent 1.29 Highest 1.87 Figure 3303. Orbital motion and displacement, s, of a particle on the surface of deep water during two wave periods

447WAVESBREAKERSANDSURF1.21.51.01.4LENGTHANDSPEED0.81.30.61.20.41.10.21.0HEIGHT--J0.90.050.100.150.200.250.300.350.400.450.50Figure 3306.Alteration of the characteristics of waves crossing a shoaltopfallingforward orbreaking.Such a wave is calledasured.Apparently,any heat that may begenerated is dissipatedbreaker, and a series of breakers is surf.to the deeper water beyond the surf zone.Swellpassing over a shoalbut not breaking undergoes3308.WaveMeasurementAboard Shipa decrease in wavelength and speed, and an increase inheight, which may be sudden and dramatic, depending onthe steepness of the seafloor's slope.This ground swellWith suitable equipment and adequate training, reli-may cause heavy rolling if it is on thebeam and its periodablemeasurements oftheheight, length,period, and speedis the sameas theperiod ofroll ofa vessel, even thoughtheof waves can bemade.However,themariner'sestimates ofsea may appear relatively calm. It may also cause a rageheight and length often contain relatively large errors.sea, when theswell waves encounter water shoal enough toThere is a tendency to underestimate the heights of lowmakethembreak.Rageseasaredangeroustosmall craft,waves,and overestimate the heights ofhigh ones.There areparticularlyapproachingfrom seaward,as thevessel canbenumerous accounts of waves 75to80feet high, or evenoverwhelmed by enormous breakers in perfectly calmhigher,although waves morethan55feet highare very rare.weather.The swell waves, ofcourse,mayhavebeen gener-Wavelength is usuallyunderestimated.The motions oftheated hundreds of miles away.In the open ocean they arevessel from which measurements are made contribute toalmost unnoticed due to their very long period and wave-such errors.length.Figure3306 illustrates the approximate alterationofHeight. Measurement of wave height is particularlythe characteristics of waves as they cross a shoal.difficult.A microbarograph can beused if the wave islongenough or the vessel small enough to permit the vessel to3307.EnergyOfWavesridefrom cresttotrough.Ifthewaves areapproaching fromdead ahead or dead astern, this requires a wavelength at leastThe potential energy ofa wave is related to the vertical dis-twice the length of the vessel.For most accurate results thetance of each particle from its stll-water position.Thereforeinstrument should beplaced atthe center ofroll andpitch,topotential energy moves with the wave. In contrast, the kineticminimize the effects of these motions.Wave height can of-energy ofa wave is related to the speed of the particles, distribten be estimated with reasonable accuracyby comparing itutedevenlyalongtheentirewave.with freeboard of the vessel. This is less accurate as waveTheamount ofkinetic energy in a wave istremendous.Aheight and vessel motion increase.If a point of observation4-foot, 10-second wave striking a coast expends more thancan be found at which the top of a wave is in line with the35,000horsepowerpermileofbeach.Foreach56milesofhorizon when the observer is in the trough, the wave heightcoast, the energy expended equals the power generated atis equal to height ofeye.However, ifthe vessel isrolling orHoover Dam. An increase in temperature of the water in the rel-pitching, this height at the moment of observation may beatively narrow surfzone in which this energy is expended woulddifficult to determine. The highest wave ever reliably report-seem tobe indicated,but no pronounced increase hasbeen mea-edwas112feetobservedfromtheUSSRamapoin1933

WAVES, BREAKERS AND SURF 447 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 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 gener￾ated hundreds of miles away. In the open ocean they are almost unnoticed due to their very long period and wave￾length. Figure 3306 illustrates the approximate alteration of the characteristics of waves as they cross a shoal. 3307. Energy Of Waves The potential energy of a wave is related to the vertical dis￾tance 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, distrib￾uted 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 rel￾atively narrow surf zone in which this energy is expended would seem to be indicated, but no pronounced increase has been mea￾sured. Apparently, any heat that may be generated is dissipated to the deeper water beyond the surf zone. 3308. Wave Measurement Aboard Ship With suitable equipment and adequate training, reli￾able 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 of￾ten 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 report￾ed was 112 feet observed from the USS Ramapo in 1933. Figure 3306. Alteration of the characteristics of waves crossing a shoal

448WAVES,BREAKERSANDSURFLength.The dimensions of the vessel can be used togravity (32.2 feet per second per second), and d is the depthdetermine wavelength.Errors are introducedbyperspectiveof water infeet.This formula is applicabletoanywaveinanddisturbanceofthewavepatternbythevessel.Theseer-water having a depth of less than half the wavelength.Forrors are minimized if observations are madefrommostocean waves it appliesonly in shallowwater,becausemaximum height.Bestresults areobtained ifthe sea is fromof the relatively short wavelength.dead ahead or dead astern.Whenatsunamienters shoal water,itundergoes thesamePeriod. If allowance is made for the motion of the vessel,changes as other waves. The formula indicates that speed is pro-wave period can be determined by measuring the interval be-portional to depth of water.Because of thegreat speed of atween passages of wave crests past the observer.The relativetsunami when it is in relatively deep water, the slowing is rela-motionofthevesselcanbeeliminatedbytimingthepassageoftivelymuchgreaterthanthatofanordinarywavecrestedbysuccessivewavecrestspastapatchoffoamorafloatingobjectwind Therefore, the increase in height is also much greater.Theatsomedistancefromthevessel.Accuracyofresultscanbeim-size ofthe wavedepends upon the nature and intensity ofthe dis-proved byaveraging several observations.turbance.Theheight and destructiveness ofthe wave arriving atSpeed.Speed canbedeterminedbytiming thepassageofany placedepends upon its distancefrom the epicenter,topogra-the wave between measured points along the side ofthe ship, ifphyoftheocean floor,and thecoastline.The angleat which thecorrectionsareappliedforthedirectionof travelforthewavewavearrives,theshape ofthe coastline,andthetopographyand the speed of the ship.along the coastand offshore,all havean effect.Theposition ofThe length, period, and speed of waves are interrelatedthe shore is also a factor, as it may be sheltered by interveningland,orbein apositionwherewaves haveatendencyto con-by the relationships indicated previously.There is no defi-nite mathematical relationship between wave height andverge,eitherbecauseofrefractionorreflection,orboth.length,period,or speed.Tsunamis 50 feet in height or higher have reached theshore,inflicting widespread damage.OnApril 1,1946.3309.Tsunamisseismic sea waves originating at an epicenter near the Aleu-tians, spread over the entirePacific.ScotchCapLight onTsunamis are ocean waves produced by sudden, large-Unimak Island,57feetabovesea level,was completelyde-scalemotionofaportion oftheocean flooror theshore,suchasstroyed. Traveling at an average speed of 490 miles peravolcaniceruption,earthquake(sometimescalledseaquakeifithour,the waves reached theHawaiian Islands in 4hoursoccurs at sea),or landslide.If they arecausedby a submarineand34minutes,wheretheyarrived as waves50feetaboveearthquake, they are usually called seismic sea waves.The pointthe high water level, and flooded a strip of coast more thandirectly above the disturbance,at whichthewaves originate,is1,000feet wide atsomeplaces.They left a death toll of 173called the epicenter. Either a tsunami or a storm tide that over-andproperty damageof s25million.Lessdestructiveflows theland is popularly called a tidalwave,although itbearswaves reached theshores of North and SouthAmerica,asnorelationtothetidewell as Australia, 6,700miles fromtheepicenter.Ifavolcaniceruption occursbelowthesurfaceof theAfterthis disaster,a tsunami warning system was set upsea, the escaping gases cause a quantity of water to bein the Pacific, even though destructive waves are relativelypushed upward in the shape of a dome.The same effect israre (averaging about one in 20 years in the Hawaiian Islands)caused bythe sudden rising of aportion of the bottom.AsThis systemmonitors seismicdisturbances throughoutthePa-thiswatersettlesback.itcreatesawavewhichtravelsatcific basin and predicts times and heights of tsunamis.high speed across thesurfaceoftheocean.Warnings are immediately sent out ifadisturbance is detectedTsunamis are a series of waves.Near the epicenter,theIn addition to seismic sea waves, earthquakes below thefirst wave may be the highest. At greater distances, thesurfaceof theseamayproducea longitudinal wavethattravelshighest wave usually occurs later in the series,commonlyupward atthespeed of sound.When a ship encounters suchabetween the third and the eighth wave.Following the max-wave, it isfelt as a suddenshock which may be so severe that theimum,they again become smaller,but the tsunami may becrewthinksthevessel has struckbottom.detectablefor several days.Indeepwaterthewaveheightofatsunamiisprobably3310.StormTidesnever greater than 2or 3feet.Since the wavelength is usu-ally considerablymorethan 1oomiles,thewaveisnotInrelatively tideless seas likethe Baltic and Mediterra-conspicuousatsea.InthePacific.wheremosttsunamisoc-nean, winds cause the chief fluctuations in sea level.cur, the wave period varies between about 15 and 60Elsewhere.theastronomicaltideusuallymasksthesevaria-minutes,andthe speed indeepwater ismorethan400tions. However, underexceptional conditions, either severeknots.The approximate speed can be computed by thefor-extra-tropical storms or tropical cyclones can producemula:changes in sea level that exceed the normal range of tide.Lowsea level isof littleconcern excepttoshipping,butaS= 0.6/gd=3.4/driseaboveordinaryhigh-watermark,particularly when it iswhere S is the speed in knots, g is the acceleration due toaccompaniedbyhighwaves,canresult inacatastrophe

448 WAVES, BREAKERS AND SURF 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 er￾rors 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 interval be￾tween 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 im￾proved 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 defi￾nite mathematical relationship between wave height and length, period, or speed. 3309. Tsunamis Tsunamis are ocean waves 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 over￾flows 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 max￾imum, 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 usu￾ally considerably more than 100 miles, the wave is not conspicuous at sea. In the Pacific, where most tsunamis oc￾cur, 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 for￾mula: 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 pro￾portional to depth of water. Because of the great speed of a tsunami when it is in relatively deep water, the slowing is rela￾tively 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 dis￾turbance. The height and destructiveness of the wave arriving at any place depends upon its distance from the epicenter, topogra￾phy 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 con￾verge, 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 Aleu￾tians, spread over the entire Pacific. Scotch Cap Light on Unimak Island, 57 feet above sea level, was completely de￾stroyed. 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 Pa￾cific 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 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. 3310. Storm Tides In relatively tideless seas like the Baltic and Mediterra￾nean, winds cause the chief fluctuations in sea level. Elsewhere, the astronomical tide usually masks these varia￾tions. 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 shipping, but a rise above ordinary high-water mark, particularly when it is accompanied by high waves, can result in a catastrophe. S 0.6 gd 3.4 d = =

449WAVES,BREAKERSANDSURFAlthough, like tsunamis, these storm tides or stormtheboundaries between water strata of different densities.Thesurges arepopularlycalled tidal waves,theyarenot associ-densitydifferencesbetweenadjacent water strata in thesea areated with the tide.They consist of a single wavecrest andconsiderably lessthanthatbetweensea andair.Consequentlyhencehavenoperiod orwavelengthinternal waves are much moreeasilyformed than surfaceThree effects in a storm induce a rise in sea level.The firstwaves.andtheyareoftenmuchlarger.Themaximumheightofwind waves on the surface is about60feet,but internalwaveis wind stress on the sea surface,which results in a piling-up ofheights as great as300feethavebeen encountered.water (sometimes called wind set-up").The second effect is theInternal waves are detected by a number of observa-convergence of wind-driven currents,which elevates the seasurfacealong the convergence line.In shallow water,bottomtions of thevertical temperature distribution, usingfriction and the effects oflocal topographycausethis elevationrecordingdevices such as the bathythermograph.They havetopersistandmayevenintensifyitThelowatmosphericpresperiods as short as a fewminutes, and as long as 12 or 24surethataccompaniesseverestormscausesthethirdeffecthours, these greater periods being associated with the tides.which is sometimes referredto asthe“inverted barometer."AnA slow-movingship,operating in a freshwater layerinchofmercuryisequivalenttoabout13.6inchesofwater,andhaving a depth approximating the draft of the vessel, maythe adjustment of the sea surface to the reduced pressure canproduce short-period internal waves. This may occur offamounttoseveralfeetatequilibriumrivers emptying into thesea,or inpolar regions in the vicin-Allthree ofthese causes act independently,and if they hap-ityofmelting ice.Under suitable conditions,thenormalpen to occur simultaneously,their effects are additive.Inpropulsion energy ofthe ship is expended in generating andaddition,the wave can be intensified or amplified by the effectsmaintaining these internal waves and the ship appears to“"stick”in the water,becoming sluggish and making littleoflocal topography.Storm tidesmay reach heights of 20feetorheadway.Thephenomenon,known asdeadwater,disapmore,and it is estimated that they causethree-fourths of thedeaths attributed to hurricanespears when speed is increasedbyafewknotsThefull significanceofinternal waves has not yet been3311.StandingWavesAnd Seichesdetermined,but it isknown that theymay cause submarinesto rise and fall likea ship at the surface,and theymayalsoPrevious articles in this chapter have dealt with progres-affectsound transmission inthesea.sive waves which appearto move regularly with time.When3314.Waves And Shipstwo systemsof progressivewaveshavingthe sameperiodtravel in opposite directions across the same area,a series ofstandingwavesmayform.Theseappeartoremain stationaryThe effects of waves on a ship vary considerably with theAnother type of standing wave, called a seiche,some-type of ship, its course and speed, and the condition of the sea.times occurs in a confined body of water.It is a long waveAshort vessel has a tendencyto ride upone side ofa wave andusuallyhaving its crest at oneend ofthe confined space,down the other side, while a larger vessel may tend to rideand its trough at the other.Its period maybe anything fromthrough the waves on an even keel. If the waves are of sucha fewminutes to an hour ormore, but somewhat less thanlengththatthebowand sternofavessel arealternatelyridingthe tidal period. Seiches are usually attributed to strongin successive crests and troughs, the vessel is subject to heavywindsordifferences inatmosphericpressure.sagging and hogging stresses,and under extreme conditionsmay break in two.A change ofheading may reduce the danger.Becauseofthedangerfrom sagging andhogging,a smallves3312.TideWavesselissometimesbetterabletorideoutastormthanalargeoneIf successive waves strike the side of a vessel at theThere are,ingeneral,two regions of high tide separatedby two regions of low tide, and these regions move progres-samephaseofsuccessiverolls.relativelysmallwavescancauseheavyrolling.The same effect,if applied to thebowsively westward around the earthas themoon revolves in itsor stern in time with the natural period of pitch, can causeorbit.Thehightidesarethecrestsofthesetidewaves.andthelowtides are thetroughs.Thewave is notnoticeableatsea,butheavy pitching.A change of either heading or speed canquickly reduce the effect.becomes apparent along thecoasts, particularly in funnel-shapedestuaries.Incertain rivermouths,orestuariesofparticAwave having a lengthtwice that of a ship places thatular configuration,the incomingwaveofhighwaterovertakesship in danger offalling off into the trough ofthe sea,partic-the preceding low tide, resulting in a high-crested, roaringularly if it is a slow-moving vessel. The effect is especiallywavewhichprogresses upstream in a surge called a borepronounced ifthe sea isbroad ontheboworbroad onthequarter.An increase of speed reduces the hazard.3313.Internal Waves3315.UsingOil ToCalmBreakingWavesThusfar,thediscussion hasbeen confinedto waves ontheHistorically oil was effective in modifying theef-surfaceofthesea.theboundarybetweenairandwater.Internalwaves, orboundarywaves,arecreatedbelowthe surface,atfects of breaking waves,and wasusefultovessels when

WAVES, BREAKERS AND SURF 449 Although, like tsunamis, these storm tides or storm surges are popularly called tidal waves, they are not associ￾ated with the tide. They consist of a single wave crest 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 pres￾sure that accompanies severe storms causes the third effect, which is sometimes referred to as the “inverted barometer.” 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 hap￾pen 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. 3311. Standing Waves And Seiches Previous articles in this chapter have dealt with progres￾sive 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, some￾times 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 differences in atmospheric pressure. 3312. Tide 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 partic￾ular configuration, the incoming wave of high water overtakes the preceding low tide, resulting in a high-crested, roaring wave which progresses upstream in a surge called a bore. 3313. 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 observa￾tions 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 vicin￾ity 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, disap￾pears 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. 3314. 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 ves￾sel 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 of speed reduces the hazard. 3315. Using Oil To Calm Breaking Waves Historically oil was effective in modifying the ef￾fects of breaking waves, and was useful to vessels when

450WAVES,BREAKERSANDSURFvessel.lowering or hoisting boats in rough weather.Its effectEnvironmental concerns haveled tothisprocedurebe-was greatest in deep water, where a small quantity suf-ficed if theoil were madeto spread to windward of theing discontinued.BREAKERSANDSURF3316.Refractiontion. This is of particular importance at entrances of tidalestuaries.When waves encounter a current running in theAs explainedpreviously,wavesare slowed inshallowopposite direction, theybecomehigher and shorter.Thisresults in a choppy sea, often with breakers.When waveswater,causingrefraction if the waves approachthebeachatan angle. Along a perfectly straight beach, with uniformmove in the same direction as current, they decrease inshoaling,the wavefronts tend to becomeparallel to theheight, and becomelonger.Refraction occurswhen wavesshore.Any irregularities inthe coastline or bottom contoursencounter a currentat anangle.however,affect the refraction,causing irregularities. In theRefraction diagrams,useful in planning amphibiousoperations,canbepreparedwiththeaidof nautical chartscase of a ridge perpendicular to the beach, for instance, theshoaling is more rapid, causinggreater refraction towardsor aerial photographs.When computer facilities are avail-the ridge.The waves tend to align themselves with thebot-able,computerprogramscanbeusedtoproducerefractiontom contours.Waves on both sides of the ridge haveadiagrams quickly and accurately.componentofmotiontowardtheridge.Thisconvergenceof3317.ClassesOfBreakerswaveenergytowardtheridgecauses an increaseinwaveorbreaker height.A submarine canyon orvalleyperpendicularIndeepwater,swellgenerallymovesacrossthesurfacetothebeach,on theotherhand,produces divergence,withadecrease in wave or breaker height.These effects are illus-as somewhat regular, smooth undulations.When shoal wa-tratedinFigure3316.Bendsinthecoastlinehaveasimilarter is reached, the wave period remains the same, but theeffect, convergence occurring at a point, and divergence ifspeed decreases. The amount of decrease is negligible untilthedepth ofwaterbecomes about one-halfthe wavelength,the coast is concave to the sea.Points act as focal areas forwave energy and experience largebreakers.Concave bayswhen the waves begin to“fee"bottom.There is a slightde-have small breakersbecausethe energyis spread out as thecrease in wave height, followed by a rapid increase, if thewavesapproachthebeach.waves are traveling perpendicular to a straightcoastwith aUnder suitable conditions,currentsalso cause refrac-uniformly sloping bottom. As the waves become higher andOWAVESNTHAa00Figure 3316.Theeffect ofbottom topography in causing waveconvergence and wave divergenceCourtesyof Robert L.Wiegel,Council onWaveResearch,University ofCaliforniia

450 WAVES, BREAKERS AND SURF lowering or hoisting boats in rough weather. Its effect was greatest in deep water, where a small quantity suf￾ficed if the oil were made to spread to windward of the vessel. Environmental concerns have led to this procedure be￾ing discontinued. BREAKERS AND SURF 3316. 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 bot￾tom 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 illus￾trated in Figure 3316. 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 refrac￾tion. 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 re￾sults 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. 3317. 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 Figure 3316. The effect of bottom topography in causing wave convergence and wave divergence. Courtesy of Robert L. Wiegel, Council on Wave Research, University of Californiia

451WAVESBREAKERSANDSURFBREANINGPOINTCACHBOTTON00BEACH ISUSUALLY VERY FLATSKETCHSHOWINGTHEGENERALCHARACTERSPILLINGBREAKEROFSPILLINGBREAKERS1AKINGPOINTERERBOTBEACN ISUSUALLYSTEEPSKETCH SHOWING THE GENERAL CHARACTERPLUNGINGBREAKEROFPLUNGING BREAKERSFOAMLINEFOAMLINEFOAMLINE0F4LOF3LofBTILWATEBAGNROTTSBEACM IS USUALLY VERY STEEPSKETCH SHOWINGTHE GENERAL CHARACTERSURGINGBREAKEROFSURGINGBREAKERSFigure3317.Thethree types ofbreakersCourtesy of RoberiL.Wiegel, Council on WaveResearch,University of California.shorter, they also become steeper, and the crest narrows.forms is determined by the steepness ofthe beach and theWhen the speed of thecrest becomesgreater than that ofthesteepness ofthe wave before it reaches shallow water, as il-wave,thefrontface of thewavebecomes steeperthanthelustrated in Figure 3317.rearface.This process continues atan acceleratingrateasLong waves break in deeper water, and have a greaterthe depth ofwaterdecreases.Ifthe wave becomes too unsta-breaker height.A steep beach also increases breaker height.ble, ittopplesforward toformabreaker.The height of breakers is less if the waves approach theThere are three general classes of breakers. A spillingbeach at an acute angle. With a steeper beach slope there isbreaker breaks gradually over a considerable distance. Agreater tendency of the breakers toplunge or surge.Follow-plunging breaker tends to curl overand break witha singleingtheuprushofwaterontoabeachafter thebreakingofawave,theseawardbackrushoccurs.Thereturningwateriscrash.Asurgingbreakerpeaksup,butsurgesupthebeachwithout spilling or plunging. It is classed as a breaker evencalledbackwash.Ittendstofurtherslowthebottomof athough itdoes notactuallybreak.Thetype ofbreaker whichwave, thus increasing its tendency to break.This effect is

WAVES, BREAKERS AND SURF 451 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 unsta￾ble, it topples forward to form a breaker. 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 il￾lustrated in Figure 3317. 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. Follow￾ing 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 Figure 3317. The three types of breakers. Courtesy of Robert L. Wiegel, Council on Wave Research, University of California

452WAVES,BREAKERSANDSURFgreater aseitherthe speedor depth ofthebackwash increas-will break in even small waves, and will isolate the long-es. The still water depth at the point of breaking isshore current.The second bar,ifoneforms,will break onlyapproximately1.3times the averagebreakerheightin heavier weather, and the third, ifpresent, only in storms.Surf varies with both position along the beach andItispossibletomoveparalleltothecoast in small craft inrelativelydeep water in the area between thesebars, be-time.Achange inposition oftenmeansa change in bottomcontour,withthe refraction effects discussed before.Atthetween the lines of breakerssame point, the height and period of waves vary consider-ably from waveto wave.Agroup of high waves is usually3319.RipCurrentsfollowed by several lower ones.Therefore,passage throughsurf canusuallybemademost easily immediatelyfollow-Asexplainedpreviously,wavefrontsadvancing overingaseriesofhigherwaves.nonparallel bottom contours are refracted to cause conver-Since surf conditions are directly related to height ofgence or divergence of the energy of the waves. Energythe waves approaching abeach,and to the configuration ofconcentrations in areas of convergence formbarriers to thethebottom,thestateofthesurfat anytimecanbepredictedreturning backwash, which is deflected along the beach toifonehasthenecessaryinformationandknowledgeoftheareas of less resistance.Backwash accumulates at weakprinciples involved. Height of the sea and swell can be pre-points, and returns seaward in concentrations,forming ripdictedfromwind data,andinformation on bottomcurrents through the surf. At these points the large volumeconfiguration can sometimes be obtained from the largestofreturningwaterhas aretarding effect upon the incomingscale nautical chart.In addition, the area of lightest surfwaves, thus adding to the condition causing the rip current.alongabeachcanbepredicted if details ofthebottomcon-Thewavesononeorbothsidesoftherip,havinggreateren-figuration areavailable.Surfpredictionsmay,however,beergy and not being retarded by the concentration ofsignificantlyin error duetothepresence of swell from un-backwash,advancefasterandfartherupthebeach.Fromknownstormshundredsofmilesaway.heretheymovealongthebeachasfeedercurrents.Atsomepoint of lowresistance,thewaterflows seaward throughthe3318.CurrentsInTheSurfZonesurf,formingtheneck oftheripcurrent.Outsidethebreakerlinethecurrentwidensandslackens,formingthehead.TheIn and adjacent tothe surf zone,currents aregeneratedvariouspartsofarip current areshown inFigure3319by waves approaching the bottom contours at an angle, andRip currents may alsobe caused byirregularities in theby irregularities in the bottom.beach face.If abeach indentation causes an uprush to ad-Waves approaching at an angle produce a longshorevance farther than the average,thebackrush is delayed andthis inturnretardsthenextincomingfoamline(thefrontofcurrent parallel to the beach, inside of the surf zone.Long-awaveas itadvances shoreward afterbreaking)atthatshore currents are most common along straight beaches.Theirspeedsincreasewithincreasingbreakerheight.depoint.Thefoam line on each side of the retarded point con-creasing wave period, increasing angle of breaker line withtinues in its advance,however, and tends to fill inthethebeach,and increasing beach slope.Speed seldom exceedsretarded area,producingarip current1 knot, but sustained speeds as high as 3 knots have been re-Ripcurrents aredangerousfor swimmers, butmaypro-corded.Longshore currents areusually constant in directionvidea clear pathto thebeachfor small craft,astheytendtoTheyincreasethedangeroflanding craftbroachingto.scour out thebottom and break through any sand bars thatWherethebottom is sandyagood distanceoffshorehaveformed.Ripcurrentsalsochangelocationovertimeasone or more sand bars typically form.The innermost barconditions change.HEADNECKYBREAKERFEED.CURRENTBEACHIDEALIZEDRIPCURRENTFigure 3319.A rip current (left) and a diagram of its parts (right)Courtesy of Robert L.Wiegel, Council on Wave Research,University of California

452 WAVES, BREAKERS AND SURF greater as either the speed or depth of the backwash increas￾es. 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 consider￾ably 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 follow￾ing 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 pre￾dicted 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 con￾figuration are available. Surf predictions may, however, be significantly in error due to the presence of swell from un￾known storms hundreds of miles away. 3318. 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. Long￾shore currents are most common along straight beaches. Their speeds increase with increasing breaker height, de￾creasing 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 re￾corded. 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 long￾shore 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, be￾tween the lines of breakers. 3319. Rip Currents As explained previously, wave fronts advancing over nonparallel bottom contours are refracted to cause conver￾gence 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 a 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 en￾ergy 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 3319. Rip currents may also be caused by irregularities in the beach face. If a beach indentation causes an uprush to ad￾vance 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 con￾tinues in its advance, however, and tends to fill in the retarded area, producing a rip current. Rip currents are dangerous for swimmers, but may pro￾vide 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 3319. A rip current (left) and a diagram of its parts (right). Courtesy of Robert L. Wiegel, Council on Wave Research, University of California