Fetch- the size of wave generation area
Fetch limited-situation
in which wave energy (or wave
height) is limited by the size of the wave generation area (fetch).
Duration
limited- situation in whih wave energy (or wave height is limited by
the duraiton of wid blowing.
Group
velocity- speed of wave proprogation.
Shallow water- water depth at which surface waves are
noticeably
attested by bottom topography.
Intermediate water- water may or may not affect by the bed.
SMB method (
this method is orginally used to compare with JONSWAP method,for
details please see the attahed excel file):
Hs=Hs(F,td,Ua,g)
Ts=Ts(F,td,Ua,g)
gHs/(Ua^2 )=f(gF/Ua^2 ,gtd/Ua)
gTs/2πUa=f(gF/Ua^2 ,gtd/Ua)
If
fetch
limit,
td>F/(C*g)
If duration limit ,
td<F/(C*g)
Note: Ua is the record wind speed, C is celerity and g is the
gravitational acceleration (9.81m/s^2)
For JONSWAP method
F^*=gF/(U_10^2
) , t^*=(gt_d)/U_10 , Feff^*=〖(t^x/68.8)〗^(3/2)
If F^*<Feff^*,
fetch limited
Hence ,
H_s^*=gHs/(U_10^2 )=0.0016*〖(F^*)〗^0.5,T_p^*=gTp/U_10
=0.286*〖(F^*)〗^(1/3)
If F^*>Feff^*,
duration limited
Hence ,
H_s^*=gHs/(U_10^2 )=0.0016*〖(Feff^*)〗^0.5,T_p^*=gTp/U_10
=0.286*〖(Feff^*)〗^(1/3)
Yao’s empirical power law:
U10/Ua=(10m/5.79m)^0.32
Note: the height (
instrument located above) for the record wind speed is 5.79m
For wave length(L):
Wave length is
calculated by trial and error method
Lo=1.56*(Ts)^2
L1=Lo√(tanh(2π/Lo*d))
L2=Lo*tanh(2π/L1*d)
L=0.5*(L1+L2)
d/L is use to determine the type of
wave (progressive wave), s= shallow water , s-IM = shallow to
intermediate water
k=wave number=(2*π)/L
n=constant for group velocity calculation=
[1/2 (1+2kd/sinh2kd) ]
Wave height (after initial wave
height by each day): Hpos2/Hpos1=[(nL)pos1/(nL)pos2]^(1/2)
Group velocity (Cg) =velocity * n
Ebar =energy density= (ρ*g*(Hs^2))/8
P=wave power= Ebar*Cg