3 Hydrodynamics
271
Fig. 3.88 The cycloid curve
z = z 0 −
h
2
e
−kz 0 cos θ
Based on the above equation, the wave shape at different water depths can
be obtained, which is plotted in Fig. 3.89. The particle circular motion speed
at a different layer is
u =
2πr
T
= r
2πg
λ
=
h
2
e
−kz 0
2πg
λ
(2) Shallow water propulsion wave (ellipse trochoid theory)
Considering that the characteristics of deepwater propulsion waves are greatly
affected by water depth, the French scientist J.V. Boussinesq (shown as
Fig. 3.89 The circle trochoid wave shape at different water depth
271
Fig. 3.88 The cycloid curve
z = z 0 −
h
2
e
−kz 0 cos θ
Based on the above equation, the wave shape at different water depths can
be obtained, which is plotted in Fig. 3.89. The particle circular motion speed
at a different layer is
u =
2πr
T
= r
2πg
λ
=
h
2
e
−kz 0
2πg
λ
(2) Shallow water propulsion wave (ellipse trochoid theory)
Considering that the characteristics of deepwater propulsion waves are greatly
affected by water depth, the French scientist J.V. Boussinesq (shown as
Fig. 3.89 The circle trochoid wave shape at different water depth