Comparison of Extreme Surface Elevation for Linear and Nonlinear Random Wave Theory for Offshore Structures

For offshore structural design, the load due to wind-generated random waves is usually the most important source of loading. While these structures can be designed by exposing them to extreme regular waves (100-year design wave), it is much more satisfactory to use a probabilistic approach to account for the inherent randomness of the wave loading. This method allows the statistical properties of the loads and structural responses to be determined, which is essential for the risk-based assessment of these structures. It has been recognized that the simplest wave generation is by using linear random wave theory. However, there is some limitation on its application as some of the nonlinearities cannot be explained when higher order terms are excluded and lead to underestimating of 100-year wave height. In this paper, the contribution of nonlinearities based on the second order wave theory was considered and being tested at a variety of sea state condition from low, moderate to high. Hence, it was proven that the contribution of nonlinearities gives significant impact the prediction of 100-year wave's design as it provides a higher prediction compared to linear wave theory.

Spectral Analysis of Nonlinear Random Wave Loadings

The spectral analysis of nonlinear random wave loadings on circular cylinders is performed in this paper by means of nonlinear spectral analysis. The study is carried out by expressing the wave profile and velocities of water particles as a nonlinear composition of the first order wave profile. Under the assumption of the first order wave profile being a zero-mean Gaussian process, the random wave spectra of finite amplitude waves are given. In order to solve the loading spectra of the finite amplitude random waves, the drag force is extended into power series of velocity. The loadings of the finite amplitude random waves are then expressed as nonlinear compositions of the first order wave profile and its derivatives. These techniques made it easier to compute the spectral densities of the finite amplitude random wave loadings.

Aspects of Nonlinear Random Wave Kinematics

Statistics of the nonlinear free surface elevation as well as the nonlinear random wave kinematics in terms of the horizontal velocity component in arbitrary water depth are addressed. Two different methods are considered: a simplified analytical approach based on second-order Stokes wave theory including the sum-frequency effect only, and a second-order random wave model including both sum-frequency and difference-frequency effects. The paper compares results for the statistics of the nonlinear free surface, and the consequences of neglecting the difference-frequency effect in the first method are discussed.