The method of analysis of Wave Track Buoy data developed by DTNSRDC is intro- 

 duced here. Some theoretical background is provided which includes parametric 

 models for directional waves and analysis based on slope. Measurements of the 

 directional waves by an orbital following buoy are presented. Finally, a 

 discussion of assumptions, practical considerations, and errors is included. 



ANALYSIS OF THE DIRECTIONAL WAVE SPECTRUM 

 METHOD OF ANALYSIS 



The expression of the two-dimensional spectrum, E(f,e), as given by 

 Longuet-Higgins , et al. is 



E(f,9) = F(f) . H(f,9) (1) 



where f is wave frequency, 9 is approaching wave direction, F(f) is the one- 

 dimensional wave spectrum component, and H(f,e) is the directional spreading func- 

 tion with 



/ H(f,e)de = l (2) 



Spreading functions can be developed by either deterministic methods or para- 

 metrical models. A conventional method to analyze the spreading function has been 

 proposed by Longuet-Higgins and associates. The spreading function is given by 

 the Fourier series as 



2 

 1 rl 



H(f,6) =- [- + I W n (a n cosnS + \ sinne)] (3) 



* 2 n=l 



where W is a weighting parameter, a and b are the Fourier coefficients in the 



expansion of H(f,9). 



Field instruments which follow the surface slope, such as cloverleaf 



buoys ' ' and discus buoys , " ' also referred to as pitch-roll buoys , measure the 



surface elevation, r\, and surface slopes, n v and ru (where r\ v - -^ and n r = -2D). 



x y x 9x y 3y 



