Non-Linear Shtp Wave Theory 
€) &5 perturbation parameters. 
p velocity potential in two dimensions 
} velocity potential of a uniform small F expansion in 3d. 
y streamfunction in 2d. 
w(f)=e-! f Pa (i) PONT CO) is the exponential integral 
n free-surface elevation above the unperturbed level 
fy g, x, r) v auxiliary variables 
g,p auxiliary functions 
ci slope of body contour 
REFERENCES 
1 Abramowitz, M. & Stegun, I. A. Handbook of Mathematical 
Functions, Dover, 1964 
2 Cole, J.D. Perturbation methods in applied mathematics, 
Blaisdell Publ. Comp. 1968 
3 Dagan, G. Nonlinear effects for two-dimensional flow past 
submerged bodies moving at low Froude numbers, Hydro- 
nautics Inc. Tech. Rep. 7103-1, 45 p. 1971 
4 Dagan, G. & Tulin, M. P. Two-dimensional gravity free- 
surface flow past blunt bodies, J. F.M., Vol. 51, p. 3; 
pp. 529-543, 1972 
5 Dagan, G. A study of the nonlinear wave resistance ofa 
two-dimensional source generated body, Hydronautics Inc. 
Tech. Rep... 7103-2, 197Za. 
6 Dagan, G. Small Froude number paradoxes and wave 
resistance at low speeds, Hydronautics Inc. Tech. Rep. 
1103-3, 1972b. 
7 Erdely, A. Asymptotic expansions, Dover, N.Y., 1956 
8 Ogilvie, T. F. Wave resistance : the low speed limit, Dept. 
of Naval Arch. & Mar. Eng. Univ. of Michigan, Rep. 
No. 002, 1968 
3 Salvesen, N. On higher order wave theory for submerged 
two-dimensional bodies, J. F.M. Vol. 38, pt. 2, pp’ 415- 
432, 1969 
1729 
