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

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DIRECTIONAL RECORDING OF SWELL FROM DISTANT STORMS 547The computed directions are shown in figures 23 and 24. Agreement with observations issomewhat disappointing. In estimating the off-shore direction of other major wave trainswe have paid attention largely to the higher frequencies which are relatively unaffectedby refraction, keeping, however, in mind the expected refraction at lower frequencies asdeveloped in this section. The essential result is that waves from east of 1800 are recorded atnearly 1800, and waves from north of 2700 at nearly 270O. Accordingly the direction of stormsin the south-east and north-west Pacific are poorly determined.280VERY lOWlFREQUENCIES00VERY HIGH|, * ~~~~~~~~~~~FREQUENCI180 200 220 240 260FIGU:RE 27. Recorded versus off-shore direction for various frequencies.Nothing has been said thus far about the relation between the recorded spectral densitiesand those in the open sea before the waves are refracted. This relation can be computedfrom the result deduced by Longuet-Higgins (1 957) that the energy density in wave-numberspace is conserved. We take the special case of a swell contained within narrow limits offrequencyf?:Wdf, and direction O+8O. The corresponding wave-number limits k+5k arereadily computed from the dispersion relation2Tff2 = gk tanh (2nkh).The problem of an off-shore source at near-shore receiver is equivalent to that of a nearshoresource and off-shore receiver, by the principle of reciprocity. At the recorder both kand 8k will be larger than in deep water (figure 30). The energy in the swell can be writtenE(l, m) kAk&8,where E(l, m) is the average energy density in the elementary area. The ratio of off-shoreenergy to recorded energy equalsko a'k0 I o I_Cr Vr a?okrE(kr m)r C VO8 r
548 W. H. MUNK, G. R. MILLER, F. E. SNODGRASS AND N. F. BARBER-~~~~~~~1800 ri:.:.:::::::::.::.:.20I .......0FIGURE 28. Ray diagram for an off-shore shoal at very low frequencies.The depth contrast is 4: 1.60 / 700 +300 +600 +9004 19o+ 1040 - ~ ~ ~ ~ ~ ~0+2020-69( -2 -10 -3 -50 900 20 40 60 80 0 10 20FIGURE 29. Left: The recorded direction 0r (relative to the shore normal) at a depth of 100 m as afunction of frequency for various directions in deep water, 00. Right: Refraction due to an offshoreshoal. Both graphs are antisymmetric about the frequency axis.where C = f/k and V = 8flfk are the phase and group velocities, respectively. The first twoterms are obtained from the known frequency and the known depth at the recording station;the ' refraction factor' 30r/500o is read off a graph such as figure 27. The method is an improvementover the customary method of measuring the variable separation between waverays that are parallel in deep water, as has been pointed out by Dorrestein ( x 960) .
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Page 25 and 26: 528 W. H-. MUNK, G. R. MILLER, F. E
Page 33 and 34: 00207'-0.C-0-01~~~~~~~~~~~~~~~~~~~~
Page 35 and 36: 538714Cld0,9~~~~~~~U0CldCIO.0a.)a.)
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Page 78 and 79: Munk et al. Phil. Trans A, volume 2

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