Physics for Geologists, Second edition

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104 Sea waves If the swell or waves enter a current flowing in the opposite direction, the wave velocity is reduced, but the energy remains the same. The wavelength is shortened and the waves become higher (as any sailor knows who has sailed in the East Australian current, or the Agulhas of SE Africa, with a stiff southerly wind). The effect seems to be quite out of proportion to the speed of the current (3-5 knots, 1.5-2.5 m s-l). Throw a stone into a smooth part of a stream and see the effect. When this swell reaches a continental shelf, it begins to 'feel' the bottom - not much at first. A typical Pacific swell has a wavelength of 200-300 m and a period of 11-14 s; Atlantic swells are shorter, being typically 50-100 m with periods of 6-8 s. The outer continental shelf is not immune to distur- bance on the sea floor due to swell because, as we have seen, there is still some movement at a depth of one wavelength. Storm waves of short wavelength have no effect at a depth of 200 m. As bottom-friction slows the wave down, its wavelength shortens. The period remains the same. The energy of the wave is not reduced significantly near the surface so it becomes higher and steeper. This continues until the wave breaks. It breaks partly because it has become too steep, and partly because of the forward motion of the orbit at the crest of the wave, the water moving faster than the wave. By this time, the effect on the bottom is considerable and sediment may be stirred up. As the wave enters shallow water, the physics changes and the velocity becomes a function of the depth of the water, d, rather than the wavelength: (gd)'l2. There is a transition from the deep-water performance to the shallow-water performance, and the full expression for wave velocity is c = J(gh/~n) tanh (2ndIh). (10.4) Water depths, d, greater than about half a wavelength are considered to be deep because the hyperbolic term approaches 1 and Equation 10.1 applies. At water depths less than about 0.05X the hyperbolic term approaches (2ndlX) and the expression reduces to the shallow-water form above, (gd)'I2. It is clear that the continental shelf is a zone of transition for the oceanic swell, and for much of it the full expression of Equation 10.4 should be used. If the waves are coming in to the coast at an angle, the inshore part of a wave is slowed relative to the off-shore part, and it is refracted. This affects the longer waves first. It is for this reason that waves come almost straight into the beach whatever the wind direction, and also the reason that a boat sheltering behind a headland rises and falls to a gentle swell rather than to waves (except the locally generated waves). A slight net lateral movement of the sand owing to the swash of waves at a slight angle to the beach can result in massive sand transport over very short periods of time in a geological context. The Polynesian navigators understood well the source and behaviour of waves, and were very skilled at detecting the various wave trains and their Copyright 2002 by Richard E. Chapman
Sea waves 105 refraction by islands. (Perhaps this is a case of natural selection at work in modern times!) Tsunami, seismic sea waves or 'tidal waves' Soon after Krakatoa, between Java and Sumatra, erupted in 1883, tidal gauges in Cape Town and Aden showed that a wave had crossed the Indian ocean at 201 m s-I (725 km h-l) to Cape Town, 156 m s-I (560 km hkl) to Aden. In 1933, an earthquake in the Japanese trench sent a wave that reached San Francisco at 210 m s-I (755 km hkl). The latter seems to imply a wavelength of over 28 km, and a period of about 135 s, or 2; minutes (but both are usually much longer, wavelengths of 100-200 km with periods up to an hour or so, and heights of about 0.5 m in open ocean). However, these waves travel at a velocity that is a function of water depth rather than wavelength - in other words, they behave as shallow-water waves Does that surprise you? It implies a mean water depth of 4 140m from Krakatoa to Cape Town, 2 470 m from Krakatoa to Aden, and 4490 m across the Pacific. Once such a wave leaves the Japanese trench, a water depth greater than h/4 is not found, so it behaves as a shallow-water wave. This has long been known, and tsunami velocities were used to estimate the mean depth of the oceans long before the oceans were surveyed. Copyright 2002 by Richard E. Chapman
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Physics for Geologists Second editi
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Copyright 2002 by Richard E. Chapma
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... vlii Contents Polarization 47 L
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Figures Copyright 2002 by Richard E
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Tables Copyright 2002 by Richard E.
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xiv Preface waves diminishes with d
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xvi Preface provides. This book is
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xviii Acknowledgements to K. Whaler
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xx Symbols mass refractive index bu
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2 Basic concepts Table 1.1 Dimensio
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4 Basic concepts Table 1.2 Basic SI
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6 Basic concepts pascal (Pa) and si
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8 Basic concepts all the relevant d
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10 Basic concepts relating them by
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2 Force The dimensions of force are
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14 Force The ratio of the Moon's ac
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16 Force Figure 2.1 The sum of the
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18 Force When a motorcycle takes a
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20 Force Figure 2.3 Torque is the p
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22 Force How does momentum differ f
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24 Force the weights - that is, the
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26 Force Figure 2.6 Wall-sticking i
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3 Gravity Universal gravity When di
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30 Gravity are significant to geolo
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32 Gravity Figure 3.2 The tractive,
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34 Gravity Mean sea level It might
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36 Gravity The benefits of space fl
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38 Gravity Figure 3.6 Profile of th
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40 Gravity Figure 3.8 The siphon at
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4 Optics Light is an electromagneti
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44 Optics Figure 4.2 Refraction. (a
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46 Optics The coeficient of reflect
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48 Optics only the light oscillatin
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50 Optics called Iceland Spar. Two
Page 69 and 70: 52 Optics Diffraction If you shine
Page 71 and 72: 54 Optics Figure 4.7 Geometrical op
Page 73 and 74: 56 Optics Figure 4.9 The mirrors in
Page 75 and 76: 5 Atomic structure and age-dating P
Page 77 and 78: 60 Atomic structure and age-dating
Page 83 and 84: 66 Electromagnetic radiation radiat
Page 85 and 86: 68 Electromagnetic radiation Source
Page 87 and 88: Heat and heat flow The noun heat ha
Page 89 and 90: 72 Heat and heat flow Second Law: A
Page 91 and 92: 8 Electricity and magnetism Electri
Page 93 and 94: Electricity and magnetism 77 Figure
Page 95 and 96: Electricity and magnetism 79 rivett
Page 97 and 98: Electricity and magnetism 8 1 defin
Page 99 and 100: Electricity and magnetism 83 is kno
Page 101 and 102: 9 Stress and strain Pressure, p, is
Page 103 and 104: Stress and strain 87 than some natu
Page 105 and 106: These three elastic constants are r
Page 107 and 108: Stress and strain 91 Figure 9.1 New
Page 109 and 110: Stress and strain 93 Figure 9.2 Com
Page 111 and 112: Stress and strain 95 Figure 9.3 Ide
Page 113 and 114: Fracture Stress and strain 97 We fo
Page 115 and 116: Stress and strain 99 from which we
Page 117 and 118: 10 Sea waves The nature of water wa
Page 119: Sea waves 103 Figure 10.1 Wave moti
Page 123 and 124: Acoustics: sound and other waves 10
Page 125 and 126: Acoustics: sound and other waves 10
Page 127 and 128: 12 Fluids and fluid flow Introducti
Page 129 and 130: Fluids and fluid flow 1 13 Figure 1
Page 131 and 132: Fluids and fluid flow 115 Figure 22
Page 133 and 134: Fluids and fluid flow 117 and the f
Page 135 and 136: water above a vertical thickness h
Page 137 and 138: Fluids and fluid flow 121 where V i
Page 139 and 140: Fluids and fluid flow 123 ardentes,
Page 141 and 142: Fluids and fluid flow 125 Figure 12
Page 143 and 144: - 14 $ 12 E 10 K .- 3 8 r cll + 6 0
Page 145 and 146: Fluids and fluid flow 129 the liqui
Page 147 and 148: Some dangers of mathematical statis
Page 155 and 156: Appendix 139 What would happen if y
Page 157 and 158: Notes 141 and since x is very large
Page 159 and 160: References Allum, J. A. E. (1966) P
Page 161 and 162: References 145 -(1950) 'Mechanism o
Page 163: Further reading 147 Trigg, G. L. an
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Physics for Geologists, Second edition

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