Wavemaking Resistance of Ships with Transom Stern 



DISCUSSION 



S. D. Sharma and L. J. Doctors 



University of Michigan 

 Ann Arbor J Michigan 



In an oral discussion at the Symposium Professor Maruo and 

 the first-named discusser challenged the validity of the author's 

 Fig. 1 because they felt that the wave profile should have been dis- 

 continuous at the location of the line sink or the pressure step, 

 X = 0, Dr. Ylm Insisted that his figure was correct, arguing that a 

 similar curve Is shown In Lcimb's "Hydrodynamics," p, 405* In 

 the meantime, we have examined the problem more closely and 

 arrived at the following conclusions. 



Let us examine the case of the pressure step first. Consider 

 a two-dimensional pressure distribution, 



p(x) =pjl +sgn(x)}/2, (Dl) 



on the mean free surface, z = 0, moving steadily with speed U 

 along the direction of Ox. The resulting motion can be described by 

 a velocity potential <^(x,z) subject to the conditions 



<^^^(x,z) +<^„{x,z) = 0, (D2) 



p(x) - pU(^,(x,0) + pg;(x) + pjjlU(^(x,0) = 0, (D3) 



U&,(x) +02(x,O) =0. (D4) 



(^^^^(x,-oo) =0, {D5) 



where z = ^(x) describes the free surface elevation and the limit 

 jt -♦ +0 is understood as usual. It is easv to verify that the solution 

 is 



•Mx.y) = - (PoApU)^ kik-^k^H^r^ ^^' ^0= g/U^ (D6) 



;(x> = - (p^pgXi +sgn(x)}/2 - i(p,Apg)y 1^^^ dk. (D7) 



601 



