Wind Energy

12 L. Bergdahl et al.
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Fig. 2.5. A solitary wave and irregular waves passing a cylinder [8]
2.6 Wave Transmission into a Shallow Area
Using Boussinesq Models
Using a phase resolving model like a Boussinesq model the surface elevation
is already in the time domain. In Fig. 2.5 snapshots of a shoaling waves passing
circular towers are shown. These simulations are made by an arbitrary
high-order finite-element method developed in [8]. The wave kinematics has,
however, to be reconstructed from the used Boussinesq assumption. However,
for the most frequently used enhanced Boussinesq models the wave kinematics
is poor. The force on the circular tower can be computed by direct integration
of the pressure on the submerged part of the structure. It may be better to
couple the enhanced Boussinesq model to a local Reynolds-Average Navier
Stokes (RANS) [9] model adjacent to the structure, taking the full viscous
and free-surface characteristics of the problem into account.
2.7 Conclusions
It has been shown that for the purpose of assessing wave loads on windpower
plants in shallow or near shore sites in the Baltic, one can establish
“deep-sea” wave climate by the Baltic WAM model, and transfer these waves
by the phase averaging wave model SWAN to the more precise position of
the plant. At this position non-linear wave kinematics can be realized in the
time-domain by a second order realization and finally the wave loading be
calculated by integrating Morison’s equation to the instantaneous free surface.
Alternatively the realized kinematics can be fed into a time-domain model e.g.
an enhanced Boussinesq model or even a local RANS model.
2.8 Acknowledgements
The wave research is funded by the Swedish Energy Administration and
FORMAS. The wind-energy application is done in co-operation with Risö
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