Practical Ship Hydrodynamics

112 Practical Ship Hydrodynamics
The distribution of the wave energy over the propagation direction f⊲ 0⊳
is independent of Uc/cp. Instead, it depends on the non-dimensional frequency
ω/ωp:
f⊲ 0⊳ D 0.5ˇ/cosh 2 [ˇ⊲ 0⊳] with
ˇ D max⊲1.24, 2.61⊲ω/ωp⊳ 1.3 ⊳ for ω/ωp < 0.95
ˇ D max⊲1.24, 2.28⊲ω/ωp⊳ 1.3 ⊳ for ω/ωp ½ 0.95
Figure 4.10 illustrates f⊲ 0⊳. Figure 4.11 illustrates ˇ⊲ω/ωp⊳.
3
2
1
2f (m−m 0 )
w/w p = 0.95
w/w p ≥ 1.6
−135 −90 −45 0 45 90 135
m−m 0
Figure 4.10 Angular distribution of seaway energy
3
2
1
0.6 0.8 1.0
b
1.2
w/wp Figure 4.11 Angular spreading ˇ
1.4 1.6 1.8
Since short waves adapt more quickly to the wind than long waves, a
changing wind direction results in a frequency-dependent main propagation
direction 0. Frequency-dependent 0 are also observed for oblique offshore
wind near the coast. The wave propagation direction here is more parallel to
the coast than the wind direction, because this corresponds to a longer fetch.