40 Observations and Measurements of Ocean Waves 



and of the wave period (Munk, 1947). It can be shown that wave periods 

 of less than 4, 8 and 15 sec are practically eliminated in depths of 40. 150 

 and 600 ft. 



The underwater unit is different for each of the instruments developed. 

 We quote Munk "As a rule, the exterior pressure variations are transmitted 

 through an outer bellows into a second bellows inside the instrument casing. 

 Thus the pressure of the air inside the two bellows always equals the pressure 

 in the water outside. The air inside the bellows can pass through a slow leak 

 into the instrument casing, so that the average pressure inside the casing, 

 equals the average pressure in the water, that is the hydrostatic pressure p h . 

 The leak is so slow that the pressure inside the instrument does not change 

 appreciably during one wave period. 



"The total displacement of the inner bellows depends on the difference 

 in pressure between the inside and the outside of the bellows and therefore 

 measures the deviations of pressure from the hydrostatic mean. These 

 deviations have an amplitude Ap. 



"For waves of very long periods the fluctuation of air pressure in the 

 instrument casing cannot be neglected. Indeed waves of tidal period are 

 almost completely eliminated from the record, as the slow leak is able to 

 compensate for the gradual rise and fall of sea level during a tidal cycle. 

 In the general case the amplitude response of the instrument is proportional 

 to r 2 /(l +r 2 ), where r = TJT. T r is the 'resonance' period, which depends on 

 the size of the slow leak, the air volume of the instrument, and the water 

 depth. T r has been assumed to equal about one hour. Owing to the combined 

 effect of hydrodynamic filtering and the slow leak, waves of short and very 

 long period are effectively eliminated. Maximum sensitivity is achieved in 

 the desired range by a proper choice of depth for the underwater unit and 

 of size for the 'slow leak'." 



The methods used for measuring waves from aboard a ship are more 

 difficult and require the ship to stop during the measurements. The dimensions 

 of the waves at the ocean surface can be derived from the movements which 

 the ship makes under the influence of the passing waves. A picture of such 

 a recording is given in Fig. 44 (p. 100). Such measurements are, of course, 

 more intricate and can only be performed on commercial ships by trained 

 personnel. 



3. Comparison between Theory and Observations 



To compare observations with theory, we need the following relations 



in metres per second: 



c = 1 25yA , c = 1 56 T, T = 0-80 M , 

 A = 64 c 2 , 7 = 064 c, A = 156T 2 . 



The fact should be stressed that a confirmation of these formulas by 



