Application of Arbitrary Lagrangian–Eulerian strips with fully nonlinear wave kinematics for force estimation

Abstract

The initial design of offshore constructions generally uses a combination of model tests and second-order wave theory to reconstruct the wave kinematics to determine wave forces using the Morison equation. This routine becomes difficult to apply to steep waves without model test data where the second-order theory is not valid. In this article, a novel approach combining a fully nonlinear numerical wave tank (NWT) using the σ-grid with strip theory and the Morison equation in an Arbitrary Lagrangian–Eulerian (ALE) framework is presented. This provides improved wave kinematics from the nonlinear numerical wave tank, an improved representation of the instantaneous velocity field associated with the instantaneous location of the free surface, making an accurate estimation of the wave hydrodynamics of highly nonlinear and breaking waves possible at a reasonable computational cost.The method is verified by comparing the calculated wave kinematics for a fifth-order Stokes wave with the analytical solution. The procedure for the estimation of the hydrodynamic loads on a cylinder is validated using comparisons with model test data for wave forces on a cylinder due to regular, irregular and focussed waves. A good agreement is seen for the estimated wave forces, including for the breaking waves in the irregular wave train. Some overestimation of the wave forces due to irregular waves is seen due to the frequency-independent force coefficient used in the Morison equation. The results demonstrate the potential of the ALE method combined with a nonlinear NWT to evaluate a three-hour irregular sea state simulation and generate wave loading statistics for the initial stochastic design of offshore structures without model test data.