3 Hydrodynamics
275
Fig. 3.92 The shape of ellipse trochoid curve under different water depth
is a changeable parameter in the equation.
x = −
λ
2π
θ + a 0 sin θ = −
λ
2π
θ +
h
2
cthk H sin θ
z = −b 0 cos θ = −
h
2
cos θ
It can also be found that the wave equation of the underwater arbitrary
wave surface is
x = −
λ
2π
θ + a sin θ = −
λ
2π
θ +
h
2
cosh k(H − z 0 )
sinh k H
sin θ
z = z 0 − b cos θ = z 0 −
h
2
sinh k(H − z 0 )
sinh k H
cos θ
Compared with the circle trochoid curve, the water peaks of the ellipse
trochoid curve are sharper and troughs are calmer. The shape curve under
different water depth is plotted at Fig. 3.92.
3.8.6 Solitary Wave
A solitary wave is a wave of limited amplitude that propagates as a single crest
or trough and can appear in shallow waters, as shown in Fig. 3.93. This kind
of fluctuation was first discovered in the laboratory by the British scientist and
shipbuilding engineer John Scott Russell (1808–1882, as shown in Fig. 3.94)
in 1844, and theoretically carried out research to propose the solitary wave