18 



Solution in Each Local Window A form for the potential function in each local 

 window is based on Fourier steady wave theory. This is the potential function used 

 by Sobey (1992): 



■. ^r ^—^ . cosYi jk{h -\- z) . .,, , ,^ „< 



Six, z,t) = Ux+y A- \ .,, sm j{kx - ut) (2.7) 



cosh jkh 



where U and h are the known depth-uniform Eulerian current and mean water depth 

 (see section 3.3.1 for a discussion of these important parameters), J is the truncation 

 order of the Fourier series, Aj are the Fourier coefficients, and u and k are the 

 local fundamental frequency and wave number. The above potential function exactly 

 satisfies mass conservation and the BBC. This form for the potential function is 

 periodic in space and time, however the periodicities are not defined apriori, but 

 found to fit the record, defining a local frequency and wave number. 



The measured record is broken down into individual segments, each in a separate 

 window in time. In each window, a diff^erent set of the parameters u;, fc, kx, and Aj 

 are found to fit the segment of the measured record. This represents that segment as 

 a piece of a larger, periodic wave. The entire record is then represented by separate 

 potential functions, each applied to a particular window in time. 



2.1.1 Dynamics 



The potential function provides the complete kinematics, and the dynamics are 

 found through the unsteady Bernoulli equation: 



^ + l-iu' + w')+gz + P-B = (2.8) 



at I p 



where p is the mass density of the water, and p is total pressure. Total pressure below 

 the water surface can be broken down into three components. Atmospheric pressure 

 (pa) is the pressure of the atmosphere at the water surface, hydrostatic pressure {ph) 

 is the pressure in the water column due to gravity, in the absence of motion. Dynamic 

 pressure {pd) is the component due to the motion of the fluid. Separating these three 

 components focuses attention on the wave motion. 



P = Pa -\- Pd -\- Ph where ph = -pgz for z < r] (2.9) 



