Tower design and analysis - Wind Power Generation and Wind Turbine Design - page 550

6.3 Joint distribution of wind and waves

The JONSWAP spectrum defi ned in the previous section is a stationary Gaussian
process and can be mapped into the process of the sea state defi ned by the sig-
nifi cant wave height and mean zero-crossing wave period ( H s , T z ) by letting the
dimensionless time be t / T z and the dimensionless process be X /

0 ) 1/2 =

4 X / H s ,
[68]. The wind speed at 10 m, U 10 , and the signifi cant wave height, H s , from the
JONSWAP spectrum can be related through the integral of eqn (24):

( l

∞

( )

∫

l = S hh w w d

(29 )

0

0

0 ) 1/2 is the standard deviation of surface displacement. If a sea contains a
narrow range of wave frequencies, H s is related to the standard deviation of the sea
surface displacement [70]:

where ( l

H = 4 l

( 30 ) s 0

The time-histories used for analysis in the joint distribution of wave period and height
are approximated by the linear combination of trigonometric polynomials [71].
Simulated wave surface elevation time-history for 'moderate' wave excitation
with target and simulated PSD have been presented for the purpose of illustration in
Figs 14 and 15 which have been taken from the investigation carried out by [65]. The
wave surface elevation time-history has been simulated with a joint dependence on

Figure 14 : Time-series for the 'moderate' wave excitation.