Directional Recording of Swell from Distant Storms - Department of ...

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Munk et al. Phil. Trans A, volume 255, plate 7"V~~~~~~~~~~~~~~~~~~~~~It~~~~~~~~~~~~~~~IV4,~~~~~~~~~~~~~~~~V(Fciq. I 5S1
DIRECTIONAL RECORDING OF SWELL FROM DISTANT STORMS 581If Em(f) denotes the mean energy in the Pacific basin and A its area, then the absorptiontime is the mean total energy divided by the mean flux:a1= Em(f) AGDWV(f) Er(f)TSet A = 2 x 108 km2, G = 10, D = 1 day, W = 103 km and r = 4 days; furthermore setV(f) 1720 km/day, Er/Em 10 for f = 40 c/ks,V(f) = 1150km/day,Er/Em = 50 for f= 60 c/ks,in accordance with the results shown in figure 43. This gives a-'40 and 60 c/ks, respectively.Suppose the energy is absorbed entirely at the boundaries. Then4 6 and 1P4 days, atACV(1-r2)'where C = 4-5 x 104km is the circumference, and r2(f) the energy reflectivity. Setting1-r2= 0 6, 0-85 at 40 and 60 c/ks, respectively, in accordance with our measurements atSan Clemente Island, we find o-' = 4-3 days and 4-5 days at the two frequencies. Theconclusion is that absorption at the boundaries is a major factor, particularly at lowfrequencies.16. THE SOUTHERN SWELLFigure 52, plate 7, shows the arrival of a 16 s wave at Oceanside, California. The inferredoff-shore direction is from 200?. In deep water these waves are above 2 ft. in height, butowing to their great length-height ratio they are amplified by a factor of about 3 before theybreak. The southern swell plays a vital role in the north Pacific basin, particularly along thecoast of California and in Hawaii. Breaking somewhat obliquely along the California shoreline the waves induce a northward littoral drift and sediment transport. Beaches representa sensitive balance between this northward transport during the months April to September(the southern winter) and a southward transport associated with waves from Alaskancyclones during the remaining year.The results in the present study may help to explain some of the known qualitativefeatures. The outstanding characteristics of the southern swell are its length, regularityand long-crestedness. It owes its length to the fact that it comes from the regions of thestrongest winds, its regularity and long-crestedness to the great distance of the storms.Dispersion leads to a cumulative sorting of frequencies so that the effective relative width ofthe frequency band is of the order (storm fetch/storm distance), or (storm duration/traveltime), which ever is larger. Typically these ratios are less than 10 % for the very distantstorms, and they may be further reduced when the storm approaches at group velocity(? 11 (c)). The regularity train- of the is intimately connected to the inverse of this ratiothe; '9' of the spectral peak. Long-crestedness, on the other hand, varies inversely with theangular spread (with the ' Q' of the beam pattern) and this parameter is large becausedistant storms subtend small angles. For swell from the Indian Ocean the beam width is
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