The Wave Generated by a Fine Shtp Bow 
that 
The final term needed is the one involving @ this quantity being 
y’ 
H 
$ Ua dé 
P, = Re} i | UP Ouene ? 
-H 
the remainder being a quantity which goes to zero at the bow. We 
need to evaluate this quantity only on z=0, for which we find 
gue (sgn y) tan ree 
We now have the following representation for the wave shape 
Zz 
4Ha 2a ARP Sal 
BE ApS 2 tan Ty] ]- ore 
The last estimate of order of magnitude is still valid in the usual 
near field, where x =O(1). In order to match this result with the 
bow-near-field formula, we must reinterpret the order of magnitude 
of x, that is, consider that x =O(e'/2), and re-order the expan- 
sion. When we do this and keep just one term, we have only 
4H 
Gy) ee = O(e7 ) 
We now observe that this matches precisely with the expression in 
(12) 
V. COMPARISON OF RESULTS WITH EXPERIMENTS 
From Equation (10), we can compute the shape of the free- 
surface disturbance : 
E507 
