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2.2 波浪 Waves

2.2 波浪 Waves. 波浪（海洋波）：海洋中最顯著之現象之一，但十九世紀後對其認知才逐漸發展。 波（廣義）：能量與動量在不同狀態藉由振動方式傳遞且介質組成粒子不前進。. 前進波 Progressive wave. 縱向 ( Longitudinal ) ：例如音波 ( Sound ) ，介質與傳遞方向平行作前後振動 ﹔ 氣、液、固體中能量均可藉縱向波傳遞。 橫向 ：能量傳遞方向與上下振動方向垂直，例如繩波。通常只發生在固體中，因唯有固體分子能如此緊繫。 圓圈向 ：水波，縱向與橫向運動特性總和。. 波浪特性. 水位最高點：波峰 ( Crest );

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2.2 波浪 Waves

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  1. 2.2 波浪Waves • 波浪（海洋波）：海洋中最顯著之現象之一，但十九世紀後對其認知才逐漸發展。 • 波（廣義）：能量與動量在不同狀態藉由振動方式傳遞且介質組成粒子不前進。

  2. 前進波Progressive wave • 縱向 ( Longitudinal )：例如音波( Sound )，介質與傳遞方向平行作前後振動﹔氣、液、固體中能量均可藉縱向波傳遞。 • 橫向：能量傳遞方向與上下振動方向垂直，例如繩波。通常只發生在固體中，因唯有固體分子能如此緊繫。 • 圓圈向：水波，縱向與橫向運動特性總和。

  3. 波浪特性 • 水位最高點：波峰( Crest ); • 水位最低點：波谷( Trough )﹔ • 波高( H )：波峰與波谷垂直距離﹔ • 波長( L )：兩波形對等點距離（例如波峰波峰）﹔ • 週期( T )：兩波形對等點經過（重複出現）時間。

  4. 深水波 ( Deep water Wave )：d / L > 1 / 2（d：水 深），波速與水分子速度直徑均隨水深遞減，約至 L / 2 深處即近似零。波長：Lo = 1.56 T2，波速：1.56 T，風波屬此類。 • 淺水波 ( Shallow water wave )：d / L < 1 / 20，海嘯（Tsunami, 地震引起）、潮波（Tidal Wave, 萬有引力），波速= ( gd )1/2 = 3.1 d1/2。 • 中間性（轉變）波 ( Transitional wave )：深水→中間→淺水1 / 20 < d / L < 1 / 2，風吹浪中大約波浪發展達週期 10 ~ 12 秒時先開始有淺化。

  5. Figure 10-1 Types of Progressive Waves Relationship of wavelength to water depth. Figure 10-3 Deep-Water and Shallow-Water Waves

  6. Ideal relations among wave speed, wavelength, and period for deep-water waves. Speed (m/s) equals the wavelength (m) divided by the period (s), or S = L/T. For example (shown with red lines), a wave with a period of 8 s has a wavelength of about 100m and a speed of about 12.5 m/s (L(m) = 1.56 (m/s)T2) Figure 10-2 Speed of Deep-Water Waves

  7. Wave profile and water-particle motions of a deep-water wave, Note the diminishing size of the orbits with increasing depth below the surface. Figure 10-3 Deep-Water and Shallow-Water Waves

  8. 風浪 Wind-Generated Waves • 風吹於海面（海：Sea）由於壓力與剪應力作用會先造成小圓波（L < 1.74 cm），或稱為毛細管波 ( capillary wave )，主要之回復力：表面張力。回復力意義：摧毀波形使海面恢復平靜（當海面受風作用而變形時）。 • 風力繼續作用時，則交互作用明顯（包括能量轉移），波形為簡諧性Sine or Cosine，回復力：重力，L = 15 ~ 35 H or H / L = 1 / 15 ~ 1 / 35。 • 風力再繼續作用時，波高( H )成長較波長( L )為快，直至H / L = 1 / 7且C = 1.2Co (Co = 1.56 T) = 1.87 T。 • C = W（風速）時不再有能量轉移（如同靜止之風），H →Hmax。

  9. As wind blows across the sea area, wave size increases with increased wind speed, fetch, and duration. As waves advance beyond the sea area, they continue to advance across the ocean surface as swell, free waves that are not driven by the wind but sustained by the energy they obtained in the sea. Figure 10-7 The Sea and Swell

  10. 故風生成浪之區域稱為海 ( Sea )，其中波浪為（多方向、不同週期與波長）。 • 三個影響風生成浪之重要因素：風速( wind speed )，延時( duration )，風域大小( fetch )。 • 一般在海中之H < 2 m，曾被確實觀測到之巨浪發生在北太平洋( Feb., 1935 ) H = 34 m, T = 14.8 s。 • 完全發展海域：風速固定，最大之海域在最大延時後波浪不再成長。 • 深海之碎波稱為：Whitecaps。

  11. As waves approach the shore and encounter water depths of less than one–half wavelengh, friction removes energy from the waves. The waves slow, stretching out so that wavelength decreases; wave height increase because the water must go somewhere, and the only way is up. When the water depth becomes 1.3 wave height, the wave reaches a steepness of 1 / 7 and breaks on the shore. Figure 10-12 Surf Zone

  12. This figure shows that most of the energy possessed by ocean waves is in wind-generated waves with a period of about 10 s. The long-period peaks on either side of the 5-minute period mark represent tsunami, while the two sharp peaks to the right represent ocean tides with their semidaily and daily periods. Figure 10-5 Distribution of Energy in Ocean Waves

  13. 湧浪 Swell • 風域之波浪速度 > 風速則波浪離開風域，波浪尖銳度變小或稱為長峰波( long-crested wave )且週期較長，稱為湧浪。 • 離散特性：傳遞至大陸棚之邊緣前能量損失小，長週期波其波速 C 較快會先離開風域，此為離散特性（一群波因波長不同而分散﹔或者說週期不同）。 • 波群特性：湧浪是以一群組合向前傳遞，深水時其波群波速 Cg為分量湧浪波速 C 之一半( 1 / 2 )。 Figure 10-6 Capillary and Gravity Waves

  14. 【波群示意圖】

  15. Figure 10-14 Refraction

  16. 干涉型態 ( Interference Pattern )：海面上湧浪前進時常會互相干擾與交會，其型態有三類分別為建設性( constructive )、毀滅性( destructive )、混合型 ( mixed )，主要是由於交會時波浪之位相或週期。 • 自由波：Swell湧浪，以被賦于之能量前進而無外力輸入。 • 強制波：Wind waves風浪，受與其相同週期之風力驅使。

  17. Figure 10-9 Wave Interference

  18. 碎波 Surf • Swell將其夾帶之能量釋放於大陸棚邊緣之碎波帶( surf zone )，由於水深變淺（淺化shoaling）→底床摩擦力增加 →波高變高、波長變短，當H / L > 1 / 7即碎波﹔故湧浪與區域風浪因波長( L )不同而碎波型態不同。 • 湧浪碎波：靠近岸邊呈現一條一條平行碎波線。 • 區域暴風浪碎波：波浪尚未完全離散，故H / L大者先碎呈不規則分佈發生，另外d ≒ 1.3Hb or Hb / d 則波浪會翻覆（碎波）。

  19. 波浪變形 Wave Transformation • A. 波浪折射 Wave Refraction 由於進入海岸地區之波浪波峰線很長，但不同時感受地形之變化， 故先感底床作用( feel bottom )者先被減速造成整體方向產生偏轉之現象。顯示波向線在岬頭處( Headland )集中造成侵蝕，在灣內( Bay )則發散造成淤積。 • B. 波浪繞射 Wave Diffraction 波浪由於結構物阻擋而轉彎繞行之現象。由於繞射使波浪能量沿波峰線（側面）分散而得以傳遞。

  20. C. 波浪反射 Wave Reflection 波浪垂直碰擊結構物而反射，兩者波長相同、方向相反而形成重複（駐）波，水分子運動仍是垂直與水平但不是橢圓形。 節點：沒有垂直水面變動之處且具有最大 水平速度﹔ 反節點：最大垂直水面變動之處且具有最大垂直速度。波浪斜向入射則形成較多小尺度且交互干涉型態，即為短峰波。 Diffraction is bending caused by waves passing an obstacle; it is not related to refraction. By diffraction, wave energy may spread to the most protected areas within a harbor. Figure 10-15 Diffraction

  21. An example of water motion viewed at four points during a wave cycle. Water is motionless when antinodes reach maximum displacement. Water movement is maximum when the water is level. Movement is totally vertical beneath the antinodes, and maximum horizontal movement occurs beneath the node. The circular motion of particles that occurs in progressive waves does not exist in standing waves. Figure 10-16 Reflection-Sanding Waves

  22. 暴潮 Storm Surge • 大型海上旋風→低氣壓→水位抬昇→隨暴風移動﹔靠岸時抬昇之水體被暴風向岸吹→Storm Surge→水位抬昇 + 大潮→大災難。 • 故Storm Surge：一團被風吹動之水體亦導致海岸地區水位抬昇﹔因而海岸災難( Catastrophe )往往是Storm Surge + High Tide + 暴風浪( Storm Waves )。

  23. 海嘯（津波，日本語）Tsunami or Seismic Sea Waves • 主因：一種巨浪，由於深海地殼內地震或地殼運動造成突然水面位移。 • 次因：地下山崩( underwater avalanche )造成。 • L ≒ 200 km屬淺水波﹔C～d（水深） > 700 km / h﹔ Ho = 0.5 m（深海中，不易察覺）但在海岸地區 H →30 m。 • 暴風 → 船進港尋求庇護，海嘯 → 使船斷纜移至深海。 • 經驗法則：先發生海岸線迅速向海側撤退，幾分鐘後即會有大浪湧至。 • 國際研究組織：ITWS : International Tsunami Warning System ; Coastal Regions of the Pacific Ocean。

  24. (a) (b) Photo ( a ) shows Sandy Beach on the Island of Oahu moments before a tsunami generated by an earthquake in Aleutian Trench Area stuck the beach. Note that the beach has been exposed as the shoreline moves out to sea. The arrow indicated the location of photo ( b ), which shows the beach a few minutes later, after the tsunami arrived. ( Photos by Y. Ishii. Reprinted by permission of Honolulu Advertiser. )

  25. Figure 10-19 Tsunami

  26. 內波 Internal Wave • 表面波：存在大氣與海水交界面處（屬密度不連續處）﹔ • 內波：海洋水面下密度不連續交界面處存在之波浪系統（e.g. 存在Pycnocline由於溫度急變而產生之密度急變）。 • 波高可高達一百米，發生原因可能由於潮汐、水下山崩、航行船隻造成之擾動。 • 不同於表面波，由於密度急變層上下層密度差＜＜空氣v.s. 水，故產生波所需之擾動能量很小﹔此外內波之運動基本上如同淺水波但速度遠小於表面波，其週期（大約5 ~ 8 min）或波長（約 0.6 ~ 0.9 km）卻較長。

  27. A simple internal wave moving along the density interface below the ocean surface. Figure 10-20 Internal Wave

  28. The Wedge, a wedge-shaped crest that may reach heights in excess of 8 m ( 26 ft ), develops as the result of interference between incoming waves and reflected waves near the jetty protecting the entrance to Newport Harbor, California. • A view of a wedge crest taken from the landward end of the jetty. The three dots in the water in front of the wave are the heads of body surfers waiting to catch the wave. Figure 10-17 Reflection-The Wedge

  29. 波力發電 Power from the Waves • 雖波浪是免費且源源不斷的，但設置波力發電結構於海中可能遭遇之困難為：（A）維護費貴，（B）造成海岸破壞或不平衡。 • 波力發電方式：( 1 ) 以折射原理導引波進入渦輪機中，( 2 ) 以波浪碎波產生巨大能量帶動渦輪機。

  30. Lockheed Corporation’s Dam-Atoll designed to generate electricity from wave action. ( a ) Water entering at the surface spirals down an 18 m ( 600 ft ) central cylinder to turn a turbine located at the bottom of the cylinder. Each unit is designed to produce from 1 to 2 MW. ( b ) View from above. (Countesy of Lockheed Corporation.) Figure 10-21 Dam-Atoll

  31. Simple scheme for generating electrical power from the energy contained in waves Figure B9-1-1

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