159 



height have been investigated (Rauch, 1945) (Barber and Ursell, 1948) and found 

 to be insignificant in the case of bottom -mounted gages. However, for record- 

 ers suspended near the surface from piers, errors of 10 percent or more may 

 exist. The effect of a sloping bottom has not been investigated completely. 

 Theroretical studies of short-crested wave systems (Fuchs, 1951) indicates that 

 the K factor computed from the wave period and water depth as given by long- 

 crested wave theory are the same as K factors computed from the short-crested 

 wave theory for the height of the wave directly above the wave recorder. 



DISCUSSION: Walter H. Munk 



The preceding paper by Snodgrass emphasizes the large effort that has 

 gone into the instrumentation of the 1 to 100 second range. Various combina- 

 tions of mechanical and electrical devices are well adapted here. I would like 

 to comment, however, on the entire wave spectrum. 



Consider the following classification of waves according to wave period 

 as shown in Figure 1 . 



2 , 1-2 1^4 .^6 _8 



Period 

 in sec. 



10' 



1 



10^ 

 minutes 



10"* 10" 10 



I I 1 I I 



hours days months years 



Type of 

 waves 



capillary gravity 



long-period 



trans tidal 



Methods of 

 measurement 



optical 



electro- 

 mechanical 



pneumatic 



numerical 



astro- 

 nomical 



FIGURE 1 



Classification Of Waves According To Wave Periods 

 This includes wave lengths from a fraction of a millimeter to something 

 of the order of the earth's radius. Details of such a classification have been 

 discussed elsewhere (Munk, 1952). 



For periods between 1 and .01 seconds, one obvious method would be to 

 record changes in resistance or capacitance resulting from changes in immer- 

 sion of thin vertical wires. One difficulty is the hysteresis effect due to water 

 clinging to the wire between wave crests. A more fundamental difficulty has to 

 do with a wake created by the wire itself as the water moves past the wire with 

 the orbital velocity appropriate to the longer waves present. This phenomenon 

 is closely related to the fishline problem. The important periods contained in 

 such a wake will be clustered about the period corresponding to minimum phase 

 velocity, i.e. , 0.07 seconds, and this falls right into the range of periods to be 

 measured. For this reason, it seems advisable to avoid altogether any punctur- 

 ing of the surface. This can be achieved by various optical methods, such as 

 have been used successfully in ripple tanks. There is not particular difficulty 

 in extending optical methods to periods as short as 0.01 seconds. Waves of 

 even shorter periods are so greatly damped by viscous dissipation that I do not 

 think they can be important. But this remains to be seen. 



To detect the very low waves with periods between 10^ and 10 seconds, 

 it seems advisable to reduce by means of suitable filters the higher swell, and 



