The wind generated wave conditions with the largest significant wave height for different return periods are included in Table 3-32. This wind sea conditions correspond to the maximum value in 1 hour; they can be scaled to 3-hour maxima with the factors included in Table 3-33.
Table 3-32 Extreme wind sea conditions /11/.
Return period/ 1 year 10 years 50 years 100 years 10000 years
Table 3-33 Correction factor from 1-hour to 3-hour maximum wind sea significant wave height /11/.
Return period Correction factor from 1-hour to 3-hour maximum Hs
1 year 0.917
10 years 0.934
50 years 0.942
100 years 0.945
10000 years 0.959
Suggested wind waves spectral parameters are included in Table 3-34.
Table 3-34 Wind wave spectral parameters according to the Metocean design basis /11/.
Parameter Recommended value
Spectrum JONSWAP with average spectral width (O=0.07 and OP=0.09) JONSWAP peakedness factor Between 1.8 and 2.3
Spreading function exponent (cosn) Between 3 and 8
Swell
The maximum swell significant wave height for different return periods is included in Table 3-35. The swell significant wave height shall be scaled for peak periods below 12 seconds as defined in Table 3-36.
In addition, a factor of 0.917 shall be used to convert from the 1-hour to the 3-hour maximum swell significant wave height.
Table 3-35 Extreme swell conditions /11/.
Return period 1 year 10 years 50 years 100 years 10000 years
Significant wave height [m] 0.22 0.28 0.33 0.34 0.46
Table 3-36 Swell significant wave height scaling factor
Swell peak period [s] Swell significant wave height scaling factor [-]
6 0.50
Suggested wind waves spectral parameters are included in Table 3-37.
Table 3-37 Swell spectral parameters according to the Metocean design basis /11/.
Parameter Recommended value
Spectrum JONSWAP with average spectral width (O=0.07 and OP=0.09) JONSWAP peakedness factor Between 3 and 5
Spreading function exponent (cosn) Between 10 and 20
Mean swell direction Between 300 and 330 degrees
Wind
Extreme wind speeds for different return periods are specified in Table 3-38; they shall be scaled depending on the incoming direction with the factors included in Table 3-39.
Table 3-38 Extreme wind speeds according to the Metocean design basis /11/.
Return period Maximum 1-hour average wind speed [m/s]
Maximum 3-hour average wind speed [m/s]
Table 3-39 Extreme wind speed directional correction factor.
Direction Reduction coefficient
345°-15° 0.7
The wind profile specified in the Metocean design basis /11/ is given as
1Q) = 1Q) ∗ S TP∗ 24.3 , (3-10)
where V(z) is the 1-hour average wind speed at height z and 1Q) = X∗ ln 1[[\) and S TP= ])^_∗`a 1^ `a1)^S))
)^_∗`a 1^ `a1b.cd))eH , (3-11)
where z0=0.01, kT=0.17, K=0.2, n=0.5 and p=1-exp(-1/T) where T is the return period in years.
The turbulence intensity for winds from 0°-150° and 210°-360° of the along wind component Iu is set in accordance with the Metocean design basis to
f== gg
ln 1 QQb) (3-12)
where ktt=1.0, z0=0.01 and z is the height above sea level. As the mean wind speed V(z) also is
proportional to ln(z/z0), the standard deviation O= of the wind component within a stationary time period is constant with height, i.e.
O== f=∗ .h= gg X S TP∗ 24.3 = 4.29 /@ 1J j 100 k0(j j0 lj m0jB n) (3-13) The standard deviation given in the Metocean design basis is assumed here to be representative for a stationary 10 minutes period. Since the analyses of the floating bridge will be performed on 3-hour periods, the 3-hour long wind fields will contain fluctuation at a larger range of frequencies (i.e. the wind field will contain also slower fluctuations). To maintain the energy level contained in the higher frequencies, it is necessary to increase the standard deviation of the wind time series. The required scaling factor is found by the ratio between the integral of the frequency spectrum in the frequency range f=[1/3hour, inf] and the range f=[1/10min, inf]:
O=, o = O=,)b h Hp qruv )ot s qruv )t s
)bh H
(3-14)
where Si is the power spectral density, see below. For the P50 spectrum specified in the MDB, the factor is found to be 1.024, resulting in a 3-hour standard deviation of O=, o = 4.39 /@. The effect of this correction is considered to be minor.
The turbulence intensity for winds from 150°-210° is high on the southern side of the fjord before becoming more steady during the travel across the fjord. In the Metocean design basis, the turbulence intensity is specified as given in Table 3-40. It is further stated that linear interpolation can be used between 50 m and 200 m above sea level.
Table 3-40 Turbulence intensities for southerly winds (coming from 150°-210°) Sector/Height above sea level Turbulence Intensity, Iu
10 m - 50 m Linearly decreasing from 30% at southern tower to 17% in
the north
200 m 15%
In TurbSim, the wind field is generated in three dimensions: a two-dimensional plane (y,z) and a time dimension. The third spatial dimension is, when the wind field is imported in Sima, taken as the time dimension with a one-to-one conversion based on the mean wind speed. This implies that a variation in turbulence intensity along the wind direction is not possible to model with the present modelling tool. As a conservative approach, the wind along the bridge is therefore modelled with a constant turbulence intensity along the bridge corresponding to the largest turbulence intensity (30% at 50 m height). The standard deviation of the u-component is constant with height and across the wind field in the present analyses.
Regardless of wind direction, the transverse and vertical turbulence components Iv and Iw are set (in accordance with the Metocean design basis) to
wffGxy = z0.840.60}f= (3-15)
The one-point frequency spectra Si(n) for all wind components are specified in the Metocean design basis as
O =s ~ •
11 + 1.5~ • )•/ for B = l, ., … , (3-16)
where Ai is the spectral density coefficient, O is the standard deviation of the wind component and
• = A
1Q) (3-17)
where n is the frequency and A is an integral length scale parameter. The different parameters in this specification are given at 50 m above ground level in Table 3-41. In an e-mail from SVV /22/, it was clarified that the spectral density coefficients (Ai’s) were obtained through fitting to the observed data keeping the integral length scale parameters from N400. In other words, to best represent the spectral properties observed at site, the P10/P50/P90 value of the spectral density coefficients should be applied together with the integral length scales from N400.
In equation (5.2) of N400 /xx/, a vertical variation in the integral length scale is indicated. In a clarification from SVV /22/ it was stated that this height dependency should be considered also at this site. This leads to the following height dependent expression for •:
• = A), ] QQ)eb.
<ln ] QQbe (3-18)
where L1,I is a the reference length scale for component i, in accordance with N400, z1=10 m, z0=0.01 m, and Vc is a constant found from the wind profile (see eq. (3-10)). With these values, a factor of 1.23 between • 1Q = 15 ) and • 1Q = 50 ) is obtained as an example. This height dependency is not possible
to model in TurbSim. In the present work a reference height of 50 m is selected and used in the analyses, as this is the height at which site-specific wind data has been evaluated. The height dependency of the spectrum is negligible compared to the statistical variations of the spectral coefficients: the difference between P10 and P90 corresponds to a factor of 4.
In conclusion, the P50 values of Ai have been applied for the present analyses. The integral length scales have been set equal to the values listed in N400 (and replicated in Table 3-41 below.)
Table 3-41 Parameters for the definition of turbulence spectra and coherence functions, as specified in ref. /22/(which was a correction to /11).
The normalized co-spectra Si1,i2 (for i=u,v,w) between points 1 and 2 separated in the (y,z)-plane (normal to the main wind direction) is specified in the Metocean design basis as
†‡ˆs‰ Š1 , ∆@Œ•
Žs‰1 )sŠ1 ) = 0•m •− Œ ∆@Œ
1Q)‘ , for B), B = l, ., … ( n ’ = k, Q, (3-19) where ∆@Œ is the horizontal or vertical distance between the points. Values for Cij are given in Table 3-41.
V(z) is assumed by DNV GL to be the mean wind speed averaged at the two points.
The P10 values for Cij in Table 3-41 have been selected here, as these give a more coherent wind field than the larger values. This is assumed to give a higher global response than less coherent wind fields.
Eq. (3-19) is an exponential Davenport coherence function, where it can be noted that none of the six Cij
values are equal. In TurbSim, it is not possible to specify different coherence for vertical and horizontal separations. For the floating part of the bridge, the horizontal coherence is more important than the vertical coherence. Therefore, the vertical coherence coefficients are in practice set equal to the horizontal ones, i.e. Cuz=Cuy=6.4, Cvz=Cvy=3.0, and Cwz=Cwy=4.5.
In TurbSim, a more general expression than eq. (3-19) is implemented. The “IEC Coherence” model, which is applied here, is given as
†‡ˆs‰ Š1 , ∆@•
Žs‰1 )sŠ1 ) = 0•m “−( ”• ∆@
•o=P‘ + 1– ∆@) — , for i = l, ., … . (3-20)
where •o=P is the mean wind velocity at “hub height”, which in practice is the height of the middle of the defined wind field. This value is therefore not varying across the wind field, in contrast to the coherence function defined in eq. (3-19). In the wind field applied in the present analyses, the •o=P is evaluated at a height of 42.5 m, which leads to a slight increase in the coherence for most of the bridge girder.
However, this effect is small compared to the variation in coherence represented by the P10 and P90 values in Table 3-41. Another limitation in the TurbSim implementation is that it is not possible to set bi
to zero. Hence, it is set as low as possible in the present analyses (bi=0.00001). As can be seen in Figure 3-23, the effect of this is negligible.
Figure 3-23: Coherence function for u-component, for horizontal separations (∆y). The shadowed areas represent P10 to P90 values as given in the Metocean design basis /11/.