Table 17.3 Neutral Drag Coefficients over the OceanaWind speed CDN(10)range rangeSource (m s-1) ( x 103) CommentsA. Miller (1964) 17-52 1.0-4.0 Hurricanes Donna(linear) and Helene-ageostrophicB. Hawkins and Rubsam (1968) 23-41 1.2-3.6 Hurricane Hilda-(discontinuous) ageostrophicC. Riehl and Malkus (1961) 15-34 2.5 Held constant toachieve angularmomentum balanceD. Palm6n and Riehl (1957) 5.5-26 1.1-2.1 Composite Hurricane(linear) data-ageostrophicE. Kunishi and Imasoto (see Kondo, 1975) 14-47.5 1.5-3.5 Wind flume experimentF. Ching (1975) 7.5-9.5 1.5 Vorticity and massbudget at BOMEXa. Taken from the literature, for hurricane and vorticity-mass-budget data analyses. Also included are wind flume data ofKunishi and Imasoto (see Kondo, 1975). [After Garratt (1977), who compiled and evaluated the source material.]C x 10'0I I I I I 0-3'.3 6 6 5 2 60 I 5 2 5 3 3 2l I I 10 20 30 40V (ms'.Figure I7.3 Mean values of the neutral drag coefficient as afunction of wind speed at 10-m height for 5-m-s-' intervals,based on individual data from hurricane studies (O), windflume experiment (), and vorticity mass budget analysis(A)-see table 17.3. Vertical bars as in figure 17.2. The numberof data contained in each mean is shown below each meanvalue, and immediately above the abscissa scale. The dashedcurve represents the variation of CDN(10) with V based on z0=au2/g with a = 0.0144. (Garratt, 1977.)Although our knowledge of the complicated proc-esses in the interfacial layer is very unsatisfactory, wecan, by using similarity theory and empirical knowl-edge of z0, ze, etc., derive formulas from which thesurface fluxes can be estimated from ships' observa-tions in the near-surface layer of, say, temperature,humidity, and wind speed at a known height, togetherwith sea-surface temperature. The errors in such esti-mates will be considerable, but they are more likely tobe due to the errors in the ships' observations than todeficiencies in the formulas.Calculations of the fluxes from climatological data[Jacobs (1951), Privett (1960), Budyko (1956), and morerecent work by Bunker (1976) and Saunders (1977)] areof great value even though their accuracy is limited bythe low precision of the ships' observations and by lackof uniformity of their cover of the ocean. They arethought unlikely to provide estimates from which thepoleward heat transport by the ocean can be deduced,but will be useful in attempts to interpret the work ofOort and Vonder Haar (1976).17.4 WavesThe most obvious effect of the wind on the sea is thegeneration of waves. They have been much studied, forthere is no doubt of their economic importance: thedesign of ships, of harbors, and of sea defenses all needestimates of the waves to be encountered, to say noth-ing of the questions raised by the reflection of soundand light at the sea surface.What is less obvious is how they fit into the coupledmechanics of the ocean and the atmosphere-how thewinds and currents would differ if by some magic de-vice the surface waves were eliminated. The drag coef-490H. Charnocki:_ .-5ficient for surface friction seems to be largely inde-pendent of the larger waves, as do the exchangecoefficients for heat and water vapor. The transfers ofenergy and momentum from the atmosphere to waveson the ocean have been studied extensively: consider-able progress has been made but there is still no com-plete agreement about the complicated fluid mechanicsinvolved.The wartime work, well confirmed and extended bySnodgrass and his colleagues (1966), established thebasic fact that swell traveled thousands of kilometers,at the theoretical group velocity, without much atten-uation. This implied that waves did not interactstrongly with each other, or with ocean currents, sothat a Fourier spectral representation was physicallyappropriate as well as mathematically convenient.From it one can derive all the statistical distributionsof the waves for which the model is valid (Longuet-Higgins, 1962). From a practical point of view we mustlearn how to recognize and circumvent the limitationsimposed by nonuniformity of the wind structure, andhow to predict the evolving (directional) wave spec-trum from such meteorological observations as areavailable, or from the output of computer simulations.17.4.1 The Fetch-Limited CaseAn important but relatively easily realizable case isthat of a steady wind blowing off a straight shore, sothat the duration of the wind is irrelevant and the fetchis well defined. An early contribution to this problemcame from Burling (1959), who measured wave spectraat short fetches on an artificial lake using a newlydeveloped capacitance-wire wave recorder.In this case one can hope that the energy of thewaves at a given fetch will be proportional to the workdone by the wind on the water. If this is crudely esti-mated as proportional to the shearing stress times adistance measured by the fetch, then= constant x u,(X/g)"2(17.17)where 2 is the mean square wave amplitude, and X thefetch.Burling's results supported the simple relation (Char-nock, 1958b) and it was confirmed for longer fetch bythe results of the JONSWAP experiment (Hasselmannand colleagues, 1973). The Joint North Sea Wave Proj-ect (JONSWAP) was an important cooperative venturein which a group of scientists from several countriespooled their observational resources to obtain wavespectral data good enough to allow generalization aboutits evolution with varying wind and fetch. They useda linear array of wave sensors spaced along a 160-mprofile extending westward from the island of Sylt inthe North Sea (figure 17.6).As regards the wave energy the JONSWAP data sup-ported (17.17). Figure 17.4, from Phillips (1977a), showsBurling's observations together with those of JON-SWAP: it is plotted in terms of nondimensional coor-dinates proposed by Kitaigorodskii (1962) to show thatthe constant of (17.17) is about 1.26 x 10-2.Burling was also able to calculate spectra. The pho-tographic recording technique and the analogue spec-tral analyzer then in use much increased the effortneeded, while restricting the precision of the estimates.Nevertheless Burling was
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