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Chapter 10 Ocean Waves Part 2

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  1. Chapter 10 Ocean Waves Part 2 ftp://ucsbuxa.ucsb.edu/opl/tommy/Geog3awinter2011/

  2. Wave orbitals for deep water waves

  3. Orbital motion of a wave

  4. FIGURE 10-9: Wave orbitals for (a) deep-waves. Deep-water waves are defined as waves traveling in water depths greater than ½ the wavelength. Deep-water Case: h > L/2 case

  5. FIGURE 10-9: Wave orbitals for (a) deep-, (c) intermediate and (d) shallow-water waves. Deep-water waves are defined as waves traveling in water depths greater than ½ the wavelength. Intermediate water waves are defined as waves traveling in water depths less than ½ the wavelength but greater than 1/20th the wavelength. Shallow water waves are defined as waves traveling in depths less than 1/20th the wavelength. Deep Intermediate Shallow

  6. “Shallow” water waves “Shallow” water waves are surface waves that travel in waters with depth h < L/20. Note: Tsunamis are “shallow” waves even though they often travel in deep ocean as their wavelengths are long! Note: Speed depends on depth and waves in deeper water travel faster. Note: Orbitals are elliptical

  7. Depends on T, L Depends on T, L, h Depends on h 1/2 k = 2p/L L L h > L/2 h < L/20 Figure 10-8: Mathematical formulations and limits of applicability for deep, intermediate and shallow-water waves.

  8. Transition from shallow to deep wavesSee Figure 10-8 c = (gh)1/2 c = (gL)1/2 /(2p)1/2 = gT/(2p) tanhfunction p = 3.14 As waves progress toward shoreline

  9. Wave orbitals for shallow water waves

  10. FIGURE 10-9: Wave orbitals for (a) deep-, (c) intermediate and (d) shallow-water waves. Deep-water waves are defined as waves traveling in water depths greater than ½ the wavelength. Intermediate water waves are defined as waves traveling in water depths less than ½ the wavelength but greater than 1/20th the wavelength. Shallow water waves are defined as waves traveling in depths less than 1/20th the wavelength. Deep Intermediate Shallow Shallow-water Case: h < L/20

  11. Wave steepness and breaking

  12. See Fig 10-20. Surf Zone: What happens to wave speed and steepness as waves move into shallower waters? If h decreases, then c decreases as c = (gh)1/2; L decreases; H increases; S = H/L increases; when S reaches a value of S =1/7, wave breaks

  13. Steepness S = H/L When S>1/7 or S > 0.14, waves typically break. Check out three examples at right. Figure 10-16 4/25=.16

  14. Breakers: What value is wave steepness for this breaker?

  15. Practice Problems on Shallow and Deep Water Waves

  16. Given a simple or ideal wave with: Wavelength L = 20 m Wave height H = 2 m Water depth h = 200 m Is this a shallow or deep water wave? h

  17. Given a simple or ideal wave with: L = 20 m H = 2 m h = 200 m Is this a shallow or deep water wave? Is h < L/20 or h>L/2? h/L = 200 m/20m = 10; h/L = 10 or h =10 L and h > .5 L or L/2 Thus, deep water wave.

  18. Since this is a deep water wave, • Does the phase speed depend on T, L, or h? • What are the wave orbital shapes? • What is the wave steepness for this wave?

  19. Since this is a deep water wave, • Does the phase speed depend on T, L, or h? • What are the wave orbital shapes? • What is the wave steepness for this wave? • Recall: • S = H/L • and H = 2 m and L = 20 m • So, • S = 2 m/20 m = 1/10

  20. Since this is a deep water wave, • Does the phase speed depend on T, L, or h? • What are the wave orbital shapes? • What is the wave steepness for this wave? • Recall: • S = H/L • And H = 2 m and L = 20 m • So, • S = 2/20 = 1/10 • Has this wave broken?

  21. Since this is a deep water wave, • Does the phase speed depend on T, L, or h? • What are the wave orbital shapes? • What is the wave steepness for this wave? • Recall: • S = H/L • And H = 2 m and L = 20 m • So, • S = 2/20 = 1/10 • Has this wave broken? • Is S> 1/7?

  22. Since this is a deep water wave, • Does the phase speed depend on T, L, or h? • What are the wave orbital shapes? • What is the wave steepness for this wave? • Recall: • S = H/L • And H = 2 m and L = 20 m • So, • S = 2/20 = 1/10 • Has this wave broken? • Is S> 1/7? • No! • Therefore not breaking yet.

  23. Try creating a similar problem that results in a shallow wave answer.

  24. Wave interference and rogue waves

  25. Fig. 10-10 Wave superposition and interference patterns: “Constructive” vs. “Destructive” vs. “Mixed” Example of two waves with same wavelengths and periods

  26. Wave interference seen in intersecting wave fields

  27. “Rogue waves” along the “wild coast” off South Africa:Wave-current interactions From Surf Science

  28. USS Ramapo in heavy seas in 1933. H = 500 sin q q = 130 q q H = H L = 500 feet L H = L sin q There are some other more recent observations of around 30 m (~100 ft) waves from ships and satellites (Google ‘rogue waves’). For example, Queen Mary, Queen Elizabeth II, and R/V Discovery have been hit by waves of >28m.

  29. The aircraft carrier Bennington:Hit by wave over 54ft high during typhoon off of Okinawa at end of WWII in 1945

  30. Seven US Navy Destroyers lost in 1923 near Pt. Arguello north of SB Channel

  31. Santa Barbara Channel region Shipwrecks: Why so many?

  32. What is a wave spectrum?

  33. Figure 10-11 A wave energy spectrum is used to display energy of waves with different frequencies, periods, or wavelengths.

  34. Wave reflection: Similar to reflection of light

  35. Wave reflection at “The Wedge”: Newport Harbor

  36. Figure 10-22 Wave reflection at “The Wedge”: Newport Harbor

  37. Wave reflection at the ‘Wedge’

  38. Wave refraction: Similar to light refraction

  39. Refraction along a straight shoreline: wave speed changes, which results from waves moving obliquely into shallower waters, causes refraction. Recall c = (gh)1/2 h decrease leads to c decrease. Like light wave refraction through glass or a a prism

  40. Longshore currents generated by refracting surface waves FIGURE 10-28: The longshore current.

  41. Waves propagate perpendicular to isobaths (lines of constant depth). Crests line up with isobaths. Figure 10-21: Wave refraction along an irregular coastline.

  42. Focusing of waves by refraction along an irregular shoreline. Examples: Palos Verdes, Campus Point, Coal Oil Point (Sands) Waves propagate perpendicular to isobaths (lines of constant depth). Crests line up with isobaths. Wave focusing on a headland.

  43. Wave shadowing by islands: Similar to light shadowing

  44. Wave shadowing

  45. Wave diffraction: Similar to light diffraction

  46. Wave diffraction of ocean surface waves Light wave diffraction is similar phenomenon: famous double slit experiments often shown in physics classes. Diffraction occurs when the size of the opening between barriers is similar to that of the wavelength of the impinging wave. Diffraction in the vicinity of islands.

  47. Rip currents, beaches, and sand movements?