APPENDIX C 
NONLINEAR WAVELENGHTS AND WAVE SPEED 
In the real-time analysis of wave reflection it is necessary to know the 
wavelength or wave speed. Linear theory gives excellent predicitons for low 
steepness waves, but tends to underestimate both length and speed for large 
waves. 
Dean (1974) gives tabular values of wave speed and wavelength for finite 
height waves that can be approximated by the empirical relation, 
ee (C-1) 
where L and C are wave speed and wavelength, L, and C, are deepwater wave 
speed and wavelength determined from linear theory where 
eT? 
aa (C-2) 
Lo = 
La is the local length determined from linear or Airy theory and a and b 
are empirical coefficients. Airy wave theory predictions and values of a and 
b are plotted as a function of d,/Ly in Figure C-l1, where d is the water 
depth. 
Ss 
2.0 40 
lg 36 
16 32 
4 
LIge halle @ a (RVLe))? oe 
2 24 
°o 
4 
“= 1.0 20 a 
S 
08 16 
06 2 
0.4 8 
0.2 be 
O (0) 
0.001 0.0! 0.1 1.0 10 
d/Lo 
Figure C-1. Coefficients for approximating nonlinear wave speed 
and wavelength determined from stream-function theory. 
40 
