(20) 



U 

 1+ — 



where U = ship's velocity. With increasing ship velocity, JJ, the apparent period 

 gets shorter. 



O^t'St for Uj c^andc^>0 (21) 



Case 2: If the wave travels in the same direction, +x , as the ship, then 

 we have 



T 



t'= (22) 



U 



X 



with 



r ^ T-'S „o for (; ^ c^ and c^ > (23) 



With ti > c^ we again have Case 1 because the phase velocity of the wave is 

 negative relative to the ship's velocity. 

 Generally, in Case 2, we find 



^r'^c<,for U| c and c >0 (24) 



Case 3 : If the wave travels with the velocity, c, in any direction which 

 makes an angle, a , with the ship's direction, then the effective ship's 

 velocity is 



Ueff^ = (J cos a (25) 



and we generally write, for the period t': 



Y _ L/cosg (26) 



with <r'^ocfor ^a = 2/7 



It is seen from equation 26 that with a = 90° we get t'= t as in the case of an 

 anchor station. 



Equation 26 shows that with no prior knowledge of the direction of 

 progress of the wave there is no possibility to filter the record because the 

 period r may appear at any value t'. In (26) the unknowns are t and a. 

 The velocity, U, of the ship is known and phase velocity of an internal wave 

 at any period is given by its eigenvalue, t' is recorded. In order to determine 

 T and a we have to carry out the cruise pattern as shown in figure 1. 



We define the angle a^ , 



V < <rr 



~cos Oq = 1 for = Qq = -2 



12 



