EM 1110-2-1100 (Part II)
30 Apr 02
Figure II-1-16. Relationship between cnoidal wave velocity and L2H/d3 (Wiegel 1960)
∆p
1
1
3∆p
1&
(II-1-87)
'
%
ρgH
2
2
ρgd
(f) Since the solitary wave has horizontal particle velocities only in the direction of wave advance, there
is a net displacement of fluid in the direction of wave propagation.
(g) The solitary wave is a limiting case of the cnoidal wave. When k2 = 1, K(k) = K(1) = 4, and the
elliptic cosine reduces to the hyperbolic secant function and the water surface ys measured above the bottom
reduces to
3 H
ys ' d % H sech 2
(x & Ct)
(II-1-88)
4 d3
(h) The free surface is given by
3 H
η ' H sech 2
(II-1-89)
(x & Ct)
4 d3
II-1-44
Water Wave Mechanics
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