Wave Forces on a Restratned Shtp tn Head-Sea Waves 
y| e (106) 
(see (96) and (98) ). In accordance with what has been done in the 
previous chapters, (106) should (for both the zero-speed and forward- 
speed cases) match with 
: ly | beg x, (2c) i( wt - vx) (107) 
where oa 1) can be written for both cases as 
a (2w +2 Up ) it /4 gh 
a, (x) = rey (x + L/2) e a (108) 
By equating (106) and (107) and putting the expression for 
B, into (105), we can write the potential 
es acces Zw +2Up ) gh i( wt - yx) 
62 wae rw v(x + L/2) upeh,« san 
Oo Oo Oo 
(109) 
Using Bernoulli's equation, it is now easy to find the pressure. 
To the leading order the pressure will be 
ap Agh ae a/2 20 FF 2° 7 ¢ ei( wt - vx) (110) 
pgh 277A) ro v(x + L/2) “u 
One should note the simple forward-speed dependence in 
(110). @, and A, will only depend on the wave length. So for a 
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