252
P. Liu
H
Fig. 3.76 Particle trajectory shape under different water depth ratio
When H /λ > 1/2, kH =
2π H
λ > π, from which, tanh(k H) = 0.9963
can be obtained, and the wave velocity is
a
2
=
g
k
=
2πg
λ
It has nothing to do with the depth of water. If the limit of shallow water
is determined in the same way, it can be reached only when kH = 0.05
tanh(k H) = k H
It can be obtained.
H
λ
=
0.05
2π
= 0.008 =
1
125
Then, at H/λ < 1/125, the wave velocity is
a
2
=
g
k
tanh(k H) = g H
Generally (as shown in Fig. 3.76):
When H/λ > 1/2 (deepwater wave);
H
λ ≤
1
200 (shallow water wave);
1
200 <
H
λ ≤
1
2 (medium water wave)
3.8.4 Linear Wave Theory (Micro Amplitude Wave
Theory)
The research of wave theory has gone through the process from regular wave
to random wave. The characteristic of regular wave theory is to take wave
motion as a definite function form and to study the dynamic properties and
P. Liu
H
Fig. 3.76 Particle trajectory shape under different water depth ratio
When H /λ > 1/2, kH =
2π H
λ > π, from which, tanh(k H) = 0.9963
can be obtained, and the wave velocity is
a
2
=
g
k
=
2πg
λ
It has nothing to do with the depth of water. If the limit of shallow water
is determined in the same way, it can be reached only when kH = 0.05
tanh(k H) = k H
It can be obtained.
H
λ
=
0.05
2π
= 0.008 =
1
125
Then, at H/λ < 1/125, the wave velocity is
a
2
=
g
k
tanh(k H) = g H
Generally (as shown in Fig. 3.76):
When H/λ > 1/2 (deepwater wave);
H
λ ≤
1
200 (shallow water wave);
1
200 <
H
λ ≤
1
2 (medium water wave)
3.8.4 Linear Wave Theory (Micro Amplitude Wave
Theory)
The research of wave theory has gone through the process from regular wave
to random wave. The characteristic of regular wave theory is to take wave
motion as a definite function form and to study the dynamic properties and