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

DIRECTIONAL RECORDING OF SWELL FROM DISTANT STORMS 571been continuous throughout the month. Evidently the flank of the mean monthly spectrumis closely related to the energy along individual ridges (figure 40) but a more detailed comparisonshows that the rise is steeper for the individual ridges (figure 43).The sharp rise in the spectrum tapers off at 50 c/ks, and the spectra] level becomes nearlyflat between 75 and 90 c/ks. At even higher frequencies the spectrum is known to rise onceagain as a result of waves generated in nearby wind systems. In figure 44 we have portrayedwhat we believe to be the typical situation. The curve marked 'distant generation' is crudelyrepresentative of the type of spectra one might expect in the generating area. Above 50 c/ksthe observed spectra fall below the expected generation spectra, and this indicates the importanceof decay processes at these higher frequencies.15. SCATTER AND ABSORPTIONThe physical processes leading to attenuation are unknown. The direct effect of molecularviscosity is negligible. The last few years have seen a rapid development in the study of nonlineareffects on wave motion; wave-wave interactions and wave-turbulence interactionhave received particular attention. In general such interactions lead to the scattering ofthe incident wave energy into waves of different lengths and/or direction. Such interactionsapply to the present study in a number of ways: forward scattering broadens the beam andaugments the spectral peaks on the low-frequency side; backward scattering reduces theenergy received at the station; scattering into high wave numbers permits molecular processesto become effective and thus ultimately leads to destruction of wave energy. The interactionsare weak and difficult to demonstrate on a laboratory scale. The present measurementsrefer to the propagation of swell over i04 wavelengths.(a) The evidence(i) Attenuation (apart from the effect of geometric spreading) appears to be small atfrequencies below 50 c/ks and predominant above 60 c/ks. This is evident both from individualridge cuts (figure 40) and the monthly spectra (figure 41). In general the spectralevel off at some fixed energy density. This suggests that the absorptive processes may beselective against the high energy rather than the high frequency. If the absorption werefrequency controlled, we should expect the spectral peaks to be slightly shifted towardslower frequencies and accordingly the ridges lines would ultimately curve to the right.Yet there is no measurable deviation from straight lines. There is no substantial broadeningof the ridge with increasing frequency (figure 45), so that the conclusion would have beensimilar had we plotted total energy under the ridge rather than energy density at the crestof the ridge.(ii) The decay following the ridges is best studied by a series of cuts at fixed frequencies(figure 46). The energy rises rapidly to the summit and then decays gradually. For example,during 5 to 7 September at 50 c/ks, the energy rose by a factor of 30 in 1 day, then decayed bya factor of 1 0 per day for the next 2 days. On 17 September at 45 c/ks the decay by a factor 10takes place in 0 7 day. The most rapid decay is associated with the event of 12-4 May(factor of 10 in 0 4 day), but this appears to be an exceptional case (? 1 1 (c) ). We shall take2 day as the typical decay time, i.e. the time for the energy to decay by a factor e. The directionof the optimum point source remains fairly constant during the decay though there