EM 1110-2-1100 (Part II)
30 Apr 02
Figure II-1-19. Influence of a uniform current on the maximum wave height
(Dalrymple and Dean 1975)
(4) It is necessary to know the limiting value of wave heights and wave steepness at different water
depths to establish range of validity of any wave theory that uses a Stokes-type expansion. This is
customarily done by comparing the magnitude of each successive term in the expansion. Each should be
smaller than the term preceding it. For example, if the second term is to be less than 1 percent of the first term
in the Stokes second-order theory, the limiting wave steepness is
sinh3 kd
H
1
#
(II-1-112)
L
80 cosh kd (3 % 2 sinh2 kd)
(5) If the third-order term is to be less than 1 percent of the second-order term, the limiting wave
steepness is
sinh3 kd
H
1
#
(II-1-113)
L
7
1 % 8 cosh3 kd
Water Wave Mechanics
II-1-57
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