157 



well as the statistical properties of the record; the correlogram therefore is 

 useful in describing the propagation of waves, predicting of surface waves from 

 sub-surface pressure, predicting the future time history of wave records from 

 the past time history and describing statistical properties of the waves, such as 

 distribution of height and period. 



ANALYSIS OF SUB-SURFACE PRESSURE RECORDS 



To obtain the surface wave heights from the pressure record, two factors 

 are required, (1) calibration of the instrument and (2) the pressure response fac- 

 tor relating the sub-surface pressure fluctuations to the surface wave. Thus if 

 H = wave height at the surface, in feet, 

 c^ = calibration factor of the instrument, expressed in feet of water 



pressure per chart division 

 K = pressure response factor based on the depth of the instrument, 

 the depth of the water and the length, or period, of the wave be- 

 ing recorded, and 

 R.: reading of the instrument, 

 the following equation is used to obtain the surface wave height: 



H = C^/K (Ri). 



The calibration factor for most instruments in use today is a constant, 

 which is independent of wave period and depth of the instrument. The instrument 

 provides a record of the pressure variations at the instrument which is accurate 

 in amplitude and wave forin. 



The relation of the sub-surface pressure fluctuations to the surface wave 

 has been determined theoretically for two-dimensional, irrotational motion of an 

 inconnpressible fluid in the relatively deep channel of constant depth (Folsom, 

 1947). 



The response factor, K, has been shown to be 



K - cosh Zrtd/L (1-z/d) 

 cosh 2jtd/L 

 where 



z = depth at which the pressure variation is being measured, in feet, 

 d = depth of water at the instrument, in feet, and 

 L = length of the surface wave, in feet. 



When z = d, the pressure variation is measured at the bottom and equation re- 

 duces to 



K = 



1 

 cosh 2jfd/L 



In deep water, where d/L/ 0.5, and the pressure recorder is located at 

 a distance, D, below the surface of the water, the equation reduces to 



K . e- (2«Di)/L 



Pressure records do not enable a direct measurement of wave lengths; 

 the wave length must be calculated from the wave period using the following 

 equation: 



2 for,Vi 2«d 



_g_ T tanh ___ 

 2n L 



