13 



shallow water, where Cnoidal methods with polynomial vertical variation are theo- 

 retically appropriate. At the same time, it may not be applicable in transitional or 

 deep water, where Stokes type methods, based on an exponential variation in the 

 vertical, are theoretically more appropriate. In a later paper, Fenton and Christian 

 (1989) presented a simplified version of the method that required less algebraic ma- 

 nipulation, and was still found to be effective in shallow water. In this case, the local 

 wave celerity was assumed to be that given by long wave theory: 



c=v^ (1.17) 



While this is a reasonable approximation for long waves in shallow water, it was 

 not appropriate for shorter waves in deeper water, as might be expected from the 

 polynomial form and the long wave celerity. 



To find a method that could work in any depth of water, Sobey (1992) developed 

 the Local Fourier Method for Irregular waves (LFI). This approach employs a po- 

 tential function represented by a low order Fourier expansion in a small window in 

 time. It is a method derived for the analysis of a point water surface trace. Local 

 frequency, wave number, and the Fourier coefficients are sought that fit the measured 

 record and the full free surface boundary conditions. The LFI method provides the 

 complete kinematics, satisfies the full governing equations, and is successful in all 

 depths of water. A more complete description of this method follows in Chapter 2. 

 Sobey's method shows a great deal of promise, but was only applied to the analysis 

 of a water surface measurement at a single location. 



Pressure sensors are easy to deploy, and thus are often used to measure waves, 

 particularly in shallow and transitional depth water. The LFI method is extended 

 in this dissertation to the interpretation of wave measurements from a point pressure 

 sensor in Chapter 3. 



Point measurements provide no information about the directionality of the mea- 

 sured wave field. Wind seas are not uni-directional, and knowledge of directionality 

 has been shown to be very important in the prediction of the kinematics and forcing 

 of structures by real seas (Dean 1977; Forristall et al. 1978). 



Arrays of measurements are frequently used in order to capture the directional 



