Bow Waves and other Non-Linear Ship Wave Problems 



(o) 





(b) 



(d) 



)(«-«/'-!) 



(•) 



(f) 



Fig. 4. High Fr^ flow past a blunt body, (a) The physical plane; 

 (b) the complex potential plane; (c) the auxiliary C, plane; 

 (d) flow past a completely blunt shape (physical plane, 

 outer variables); (e) the body first- order boundary condition 

 in the outer expansion; (f) the zero order boundary conditions 

 in the inner expansion. 



equation 



h(x) = €h,(x) 



(17) 



at first order 



6, = € 



Re (w, + ik,) = (^ < 0, |ji = 0) 



Imk,(;) = - h,(e) (e > 0, fjL = 0) 



(18) 

 (19) 

 (20) 



where 



615 



