(x,y) location. This term is identically the phase of the plane wave when 

 t = for that (x,y) location. Rewriting the plane wave equation by 

 expanding the k-x term gives 



ry = a cos(2»rft - k^x - kyy) (A2) 



where the wave number and position vectors are converted to component form 

 (Figure Al) . The phase term in the cosine argument for t = and an 

 arbitrary (x,y) location is 



^ = k^x + kyy (A3) 



8. For two sensors located on a line parallel to the shoreline, the 

 offshore coordinates x = Xj^ and x = X2 will be the same. The longshore 

 coordinates y = yi and y = ya will differ. The sensors will have the 

 following respective phase terms 



4>i = K^i + ISrYi (A4a) 



't>z = lScX2 + kyy2 (A4b) 



A4> = <l>i - 4>2 



=\ iy^ - yz) (A5) 



since Xi = ^2 • This phase difference contains the information needed to 

 obtain the propagation direction of the wave. Application of trigonometry to 

 the vector diagram in Figure Alb gives the relation 



ky = k sin (27r5/360) (A6) 



where d is the plane wave propagation direction (in degrees), measured from 

 shore normal, and k is the magnitude of the wave number vector k . 

 Equation A5 then can be written 



A4 



and phase difference 



