Table 17 3 Neutral Drag Coefficients over the Oceana Wind speed range m s 1 Source CDN 10 range x 103 A Miller 1964 17 52 1 0 4 0 linear B Hawkins and Rubsam 1968 23 41 C Riehl and Malkus 1961 15 34 1 2 3 6 discontinuous 2 5 D Palm6n and Riehl 1957 5 5 26 E Kunishi and Imasoto see Kondo 1975 F Ching 1975 14 47 5 7 5 9 5 1 1 2 1 linear 1 5 3 5 1 5 Comments Hurricanes Donna and Heleneageostrophic Hurricane Hildaageostrophic Held constant to achieve angular momentum balance Composite Hurricane data ageostrophic Wind flume experiment Vorticity and mass budget at BOMEX a Taken from the literature for hurricane and vorticity mass budget data analyses Also included are wind flume data of Kunishi and Imasoto see Kondo 1975 After Garratt 1977 who compiled and evaluated the source material i I I I I I 0 C x 10 3 3 0 I 0 10 6 6 2 5 l I 20 2 5 3 5 I 30 6 3 5 2 40 V ms Although our knowledge of the complicated processes in the interfacial layer is very unsatisfactory we can by using similarity theory and empirical knowledge of z0 ze etc derive formulas from which the surface fluxes can be estimated from ships observations in the near surface layer of say temperature humidity and wind speed at a known height together with sea surface temperature The errors in such estimates will be considerable but they are more likely to be due to the errors in the ships observations than to deficiencies in the formulas Calculations of the fluxes from climatological data Jacobs 1951 Privett 1960 Budyko 1956 and more Figure I7 3 Mean values of the neutral drag coefficient as a function of wind speed at 10 m height for 5 m s intervals based on individual data from hurricane studies O wind flume experiment and vorticity mass budget analysis A see table 17 3 Vertical bars as in figure 17 2 The number of data contained in each mean is shown below each mean value and immediately above the abscissa scale The dashed curve represents the variation of CDN 10 with V based on z0 au2 g with a 0 0144 Garratt 1977 recent work by Bunker 1976 and Saunders 1977 are of great value even though their accuracy is limited by the low precision of the ships observations and by lack of uniformity of their cover of the ocean They are thought unlikely to provide estimates from which the poleward heat transport by the ocean can be deduced but will be useful in attempts to interpret the work of Oort and Vonder Haar 1976 17 4 Waves The most obvious effect of the wind on the sea is the generation of waves They have been much studied for there is no doubt of their economic importance the design of ships of harbors and of sea defenses all need estimates of the waves to be encountered to say nothing of the questions raised by the reflection of sound and light at the sea surface What is less obvious is how they fit into the coupled mechanics of the ocean and the atmosphere how the winds and currents would differ if by some magic device the surface waves were eliminated The drag coef 490 H Charnock ficient for surface friction seems to be largely independent of the larger waves as do the exchange coefficients for heat and water vapor The transfers of energy and momentum from the atmosphere to waves on the ocean have been studied extensively considerable progress has been made but there is still no complete agreement about the complicated fluid mechanics involved The wartime work well confirmed and extended by Snodgrass and his colleagues 1966 established the basic fact that swell traveled thousands of kilometers at the theoretical group velocity without much attenuation This implied that waves did not interact strongly with each other or with ocean currents so that a Fourier spectral representation was physically appropriate as well as mathematically convenient From it one can derive all the statistical distributions of the waves for which the model is valid LonguetHiggins 1962 From a practical point of view we must learn how to recognize and circumvent the limitations imposed by nonuniformity of the wind structure and how to predict the evolving directional wave spectrum from such meteorological observations as are available or from the output of computer simulations 17 4 1 The Fetch Limited Case An important but relatively easily realizable case is that of a steady wind blowing off a straight shore so that the duration of the wind is irrelevant and the fetch is well defined An early contribution to this problem came from Burling 1959 who measured wave spectra at short fetches on an artificial lake using a newly developed capacitance wire wave recorder In this case one can hope that the energy of the waves at a given fetch will be proportional to the work done by the wind on the water If this is crudely estimated as proportional to the shearing stress times a distance measured by the fetch then constant x u X g 2 ported 17 17 Figure 17 4 from Phillips 1977a shows Burling s observations together with those of JONSWAP it is plotted in terms of nondimensional coordinates proposed by Kitaigorodskii 1962 to show that the constant of 17 17 is about 1 26 x 10 2 Burling was also able to calculate spectra The photographic recording technique and the analogue spectral analyzer then in use much increased the effort needed while restricting the precision of the estimates Nevertheless Burling was able to establish the main features of the nondirectional frequency spectrum He found that there was a very rapid increase at low frequencies to a maximum value at frequency no determined by the wind speed and the fetch At frequencies greater than n the spectra fell off approximately as frequency 5 In this so called equilibrium range of the spectrum the energy was largely independent of both wind and fetch Figure 17 5 from Phillips 1977a includes some of Burling s spectra together with those of later workers Those of the JONSWAP project are broadly similar figure 17 6 but near the peak frequency they show an overshoot which had first been observed by Kinsman 1960 and by Barnett and Wilkerson 1967 who used an airborne radar altimeter to measure one dimensional wavenumber spectra over larger fetches Snyder and Cox 1966 had measured the evolution of one particular spectral band around 0 3 Hz by towing an array of wave recorders downwind at the appropriate group velocity finding that the energy overshot in 10 k 10o the North Sea figure 17 6 As regards the wave energy the JONSWAP data sup 17 17 where 2 is the mean square wave amplitude and X the fetch Burling s
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