## Diffraction theory

The regions of validity of the aforementioned methods for the calculation of forces on a vertical cylinder are depicted in Fig. 2.6 [143]. The double logarithmic plot shows the Keulegan-Carpenter number KC (ratio between drag and inertia force) against the relative size of the (submerged part of the) support structure. The relative size is expressed by the cross-section dimension of structure D divided by the wave length L. Both axes are limited for increasing values by the slope of the deep water breaking wave curve (L/H = 7, with L the wave length and H the wave height).

Figure 2.6: Regions of validity of the Morison equation, Froude-Krylov theory and the diffraction theory, with H the wave height, D the cross-section dimension, and L the wave length [143].

From Fig. 2.6 it can be concluded that:

• When the (submerged part of the) support structure is small compared to the predominant water wave lengths (i.e. D/L < 0.2), it can be assumed that the incident wave field is not significantly deformed by the presence of the support structure. In this case, wave loads can be calculated from the Morison equation, where the total force is simply given by the linear combination of drag and inertia forces;

• When the drag force is small and the inertia force predominates, and the structure is still relatively small, the Froude-Krylov theory can be applied;

• When the structure is not small compared to predominant wave lengths (D/L > 0.2), the incident wave field is significantly deformed by the presence of the support structure. In this case, the diffraction theory has to be used to compute the wave forces to include the effects of wave scattering around the support structure.

In Table 2.1, and Table 2.2 on page 40, and 41 respectively, it is listed which of the aforementioned design codes is equipped with a wave module. From this table it can be concluded that all codes use the Morison equation to compute the wave forces. In addition, PHATAS-IV uses ROWS (Random Ocean Wave Simulator) [314] to generate the waves.

## Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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