A non-linear stretching method was implemented for stream function theory to solve wave kinematics for physical conditions close to breaking waves in shallow waters, with wave heights limited by the water depth. The non-linear stretching method proves itself robust, efficient and fast, showing good agreement with numerical tools used in the current study; hereby, extending the practical application to load assessment for wind offshore engineering designs.
The stream function theory (SFT) has quickly become a preferable method to assess the wave kinematics because of the numerical and computational power evolution. The robustness and easy application to shallow water waves of the SFT, made it popular for practical applications. With fast results easy to apply directly into Morrison equation, is preferred for offshore industrial design, such as wind turbine foundation design. Hence, the use of resources like CFD analysis, which still requires long calculation time, can be directed toward more crucial design problems.
The upside of SFT refers to application for waves close to the breaking limit. However, the breaking criterion for shallow water with design wave heights (H) of 0.78 of water depths (h) proves to be a challenging issue. Singularity problem of the Jacobian determinant and the Fourier coefficients found for wave elevation generating secondary peaks for the derived accelerations (doubling its magnitude values) are examples of SFT limitations for extreme cases. Moreover, in practical design of offshore wind turbines foundation these design conditions are frequently encountered. Therefore, an intensive research started on this topic by checking some possible methods to extend the range of solution convergence for waves close to breaking limit for SFT.
The most common applications of the Fourier fitting coefficients for water elevation to obtain the kinematics of a wave are given in literature with respect to Dean (1965) and Fenton (2015) publications. The latter, refers to the on-line support manual for the computation programs offered by J. Fenton relating his entire work for wave theory publications.
