GUIDE WAVE ANALYSIS AND FORECASTING - WMO

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xxx Beach line xxx Isobaths xxx xxx Wave crests xxx AN INTRODUCTION TO OCEAN WAVES 5 Breakers xxx Figure 1.6 — Refraction along a straight beach with parallel bottom contours Beach line Isobaths Beach line Isobaths Bay Isobaths Orthogonals Orthogonals Headland Figure 1.7(a) — Refraction by a submarine ridge Figure 1.7(b) — Refraction by a submarine canyon Figure 1.8 — Refraction along an irregular shoreline Bay Orthogonals A further feature of changing depth is changing wave height. As a wave approaches the shore its height increases. This is a result of the changes in group velocity. The energy propagating towards the coast must be conserved, at least until friction becomes appreciable, so that if the group velocity decreases and wavelength decreases, the energy in each wavelength must increase. From the expression for energy in Section 1.2.4 we see that this means that the height of the wave must increase. 1.2.6 Refraction and diffraction As waves begin to feel the bottom, a phenomenon called refraction may occur. When waves enter water of transitional depth, if they are not travelling perpendicular to the depth contours, the part of the wave in deeper water moves more rapidly than the part in shallower water, according to Equation 1.11, causing the crest to turn parallel to the bottom contours. Some examples of refraction patterns are shown in Figures 1.6, 1.7 and 1.8. Generally, any change in the wave speed, for instance due to gradients of surface currents, may lead to refraction, irrespective of the water depth. In Section 4.5.1 a few examples are given to illustrate refraction under simplified conditions. A more complete description of methods for the analysis of refraction and diffraction can be found in Sections 7.3 and 7.4, and in CERC (1984). Finally, the phenomenon of wave diffraction should be mentioned. It most commonly occurs in the lee of obstructions such as breakwaters. The obstruction causes energy to be transformed along a wave crest. This transfer of energy means that waves can affect the water in the lee of the structure, although their heights are much reduced. An example is illustrated in the photograph in Figure 1.9. 1.2.7 Breaking waves In Section 1.2.3, it was noted that the speed of the water particles is slightly greater in the upper segment of the orbit than in the lower part. This effect is greatly magnified in very steep waves, so much so that the maximum forward speed may become not πH/T but 7H/T. Should 7H become equal to the wavelength λ (i.e. H/λ = 1/7), the forward speed of the water in the crest would then be equal to the rate of propagation which is λ/T. There can be no greater forward speed of the water because the water would then plunge forward out of the wave: in other words, the wave would break. According to a theory of Stokes, waves cannot attain a height of more than one-seventh of the wavelength without breaking. In reality, the steepness of waves is seldom greater than one-tenth. However, at values of that magnitude, the profile of the wave has long ceased to be a simple undulating line and looks more like a trochoid (Figure 1.10). According to Stokes’ theory, at the limiting steepness of one-seventh, the forward and backward slopes of the wave meet in the crest under an angle of 120° (Figure 1.11).
6 When waves propagate into shallow water their characteristics change as they begin to feel the bottom, as we have already noted in Section 1.2.5. The wave period remains constant, but the speed decreases as does the wavelength. When the water depth becomes less than half the wavelength, there is an initial slight decrease in wave height*. The original height is regained when the ratio h/λ is about 0.06 and thereafter the height increases rapidly, as does the wave steepness, until breaking point is reached: h b = 1.28 H b GUIDE TO WAVE ANALYSIS AND FORECASTING Figure 1.9 — Wave diffraction at Channel Islands harbour breakwater (California) (from CERC, 1977) 120 ° (1.13) _________ * Tracking a wave into shallow water, the wavelength decreases and the wave slows down but, initially, its energy does not. The energy then spreads over relatively more waves and the height reduces This is only temporary. The wave energy soon also slows and the height begins to increase. 7 1 Mean level in which h b is termed the breaking depth and H b the breaker wave height. 1.3 Wave fields on the ocean Figure 1.10 — Trochoidal wave profile. Here the crests project farther above the mean level than the troughs sink under it Figure 1.11 — Ultimate form which water waves can attain according to Stokes’ theory 1.3.1 A composition of simple waves Actual sea waves do not look as simple as the profile shown in Figure 1.2. With their irregular shapes, they appear as a confused and constantly changing water surface, since waves are continually being overtaken and crossed by others. As a result, waves at sea are often short-crested. This is particularly true for waves growing under the influence of the wind (wind sea). A more regular pattern of long-crested and nearly sinusoidal waves can be observed when the waves are no longer under the influence of their generating winds. Such waves are called swell and they can travel hundreds and thousands of kilometres after having left the area in which they were generated. Swell from distant generating areas often mixes with wind waves generated locally.
Page 1 and 2: WORLD METEOROLOGICAL ORGANIZATION G
Page 3 and 4: © 1998, World Meteorological Organ
Page 5 and 6: IV Chapter 7 - WAVES IN SHALLOW WAT
Page 7 and 8: ACKNOWLEDGEMENTS The revision of th
Page 9 and 10: VIII has been included particularly
Page 11 and 12: X considerable attention. Annex III
Page 13 and 14: 2 η Crest Zero level a H = 2a a Tr
Page 15: 4 Figure 1.5 — Paths of the water
Page 19 and 20: 8 1.3.2 Wave groups and group veloc
Page 21 and 22: 10 wavelengths in a given sea state
Page 23 and 24: 12 for instance, a frequency of 0.1
Page 25 and 26: 14 in which E(f) is the variance de
Page 27 and 28: 16 2.1.1 Wind and pressure analyses
Page 29 and 30: 18 GUIDE TO WAVE ANALYSIS AND FOREC
Page 31 and 32: 20 Figure 2.2(a) (right) — Usual
Page 33 and 34: 22 As a quick approximation of ocea
Page 35 and 36: 24 GUIDE TO WAVE ANALYSIS AND FOREC
Page 37 and 38: 26 Gr G Gr ∇p C Cnf ∇p C Cnf
Page 39 and 40: 28 POINT C — The effect of warm a
Page 41 and 42: 30 a general sense, and can be appl
Page 43 and 44: 32 Free atmosphere Ekman layer Cons
Page 45 and 46: 3.1 Introduction This chapter gives
Page 47 and 48: ange of directions. Also, waves at
Page 49 and 50: small enough that swell can survive
Page 51 and 52: Figure 3.7 — Structure of spectra
Page 53 and 54: 4.1 Introduction CHAPTER 4 WAVE FOR
Page 55 and 56: necessary to forecast waves for a p
Page 57 and 58: TABLE 4.4 Additional wave informati
Page 59 and 60: TABLE 4.6 Ranges of swell periods a
Page 61 and 62: this situation, the angular spreadi
Page 63 and 64: the energy flux is c gH 2 . This is
Page 65 and 66: α0, degrees Solution: 80° 70° 60
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5.1 Introduction National Meteorolo
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only once, since it is usual to sto
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Frequency 0.050 0.067 0.083 0.100 0
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The models may differ in several re
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The CH class may include many semi-
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6.1 Introductory remarks Since the
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in some applications, the zero up/d
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OPERATIONAL WAVE MODELS 71 Figure 6
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give large differences in the compa
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Wind (m/s) Waves (m) Buoy/GSOWM Wav
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TABLE 6.2 Numerical wave models ope
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TABLE 6.2 (cont.) Country Name of m
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7.1 Introduction The evolution of w
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water boundary into shallow water.
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eflected waves, although the latter
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Energy (cm 2 /Hz) Energy (cm 2 /Hz)
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8.1 Introduction Wave data are ofte
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matter and timing the intervals bet
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a Directional Waverider (Barstow et
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80°N 60°N 40°N 20°N 0° -20°S
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a combination of sea-surface temper
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8.7.1 Digital analysis of wave reco
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9.1 Introduction Chapter 8 describe
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Presentation of data and wave clima
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the monsoon season of June to Septe
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Probability of non-exceedance case
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individual wave height derived usin
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emote, data-sparse areas. However,
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TABLE 9.2 (cont.) Country Source of
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For a storm hindcast, select the mo
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TABLE 9.3 (cont.) Country Model use
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ANNEX I ABBREVIATIONS AND KEY TO SY
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Abbreviation/ Definition Symbol MOS
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CODE FORM: D . . . . D or IIiii* SE
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sensors, spectral peak wave period
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cs1cs1 The ratio of the spectral de
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M jM j n mn m n smn sm n bn bn b P
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1744 Im Indicator for method of cal
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The following distributions are bri
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4. Weibull distribution Probability
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8. Fisher-Tippett Type I (FT-I) (or
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ANNEX IV THE PNJ (PIERSON-NEUMANN-J
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ANNEX IV 141 Duration graph. Distor
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REFERENCES Abbott, M. B., H. H. Pet
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REFERENCES 145 Carter, D. J. T., P.
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REFERENCES 147 Gumbel, E. J., 1958:
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REFERENCES 149 Maat, N., C. Kraan a
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Slutz, R. J., S. J. Lubker, J. D. H
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SELECTED BIBLIOGRAPHY CERC, 1984: C
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156 Energy . . . . . . . . . . . .
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158 steepness . . . . . . . . . . .
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GUIDE WAVE ANALYSIS AND FORECASTING - WMO

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