Dramas of the sea: episodic waves and their impact on offshore structures

Abstract

For the design of safe and economic offshore structures and ships the knowledge of the extreme wave environment and related wave/structure interactions is required. A stochastic analysis of these phenomena is insufficient as local characteristics in the wave pattern are of great importance for deriving appropriate design criteria. This paper describes techniques to synthesize deterministic task-related ‘rogue’ waves or critical wave groups for engineering applications. These extreme events, represented by local characteristics like tailored design wave sequences, are integrated in a random or deterministic seaway with a defined energy density spectrum. If a strictly deterministic process is established, cause and effect are clearly related: at any position the nonlinear surface elevation and the associated pressure field as well as the velocity and acceleration fields can be determined. Also the point of wave/structure interaction can be selected arbitrarily, and any test can be repeated deliberately. Wave–structure interaction is decomposable into subsequent steps: surface elevation, wave kinematics and dynamics, forces on structure components and the entire structure and structure motions. Firstly, the generation of linear wave groups is presented. The method is based on the wave focussing technique. In our approach the synthesis and up-stream transformation of arbitrary wave packets is developed from its so-called concentration point where all component waves are superimposed without phase-shift. For a target Fourier wave spectrum a tailored wave sequence can be assigned to a selected position. This wave train is linearly transformed back to the wave maker and—by introducing the electro-hydraulic and hydrodynamic transfer functions of the wave generator—the associated control signal is calculated. The generation of steeper and higher wave groups requires a more sophisticated approach as propagation velocity increases with wave height. With a semi-empirical procedure the control signal of extremely high wave groups is determined, and the propagation of the associated wave train is calculated by iterative integration of coupled equations of particle tracks. With this deterministic technique ‘freak’ waves up to heights of 3.2 m have been generated in a wave tank. For many applications the detailed knowledge of the nonlinear characteristics of the flow field is required, i.e. wave elevation, pressure field as well as velocity and acceleration fields. Using a finite element method the velocity potential is determined, which satisfies the Laplace equation for Neumann and Dirichlet boundary conditions. In general, extremely high rogue waves or critical wave groups are rare events embedded in a random seaway. The most efficient and economical procedure to simulate and generate such a specified wave scenario for a given design variance spectrum is based on the appropriate superposition of component waves or wavelets. As the method is linear, the wave train can be transformed down-stream and up-stream between wave board and target position. The desired characteristics like wave height and period as well as crest height and steepness are defined by an appropriate objective function. The subsequent optimization of the initially random phase spectrum is solved by a sequential quadratic programming method (SQP). The linear synthetization of critical wave events is expanded to a fully nonlinear simulation by applying the subplex method. Improving the linear SQP-solution by the nonlinear subplex expansion results in realistic rogue-waves embedded in random seas. As an illustration of this technique a reported rogue wave—the Draupner ‘New Year Wave’ is simulated and generated in a physical wave tank. Also a ‘Three Sisters’ wave sequence with succeeding wave heights H s,…,2 H s,…, H s, embedded in an extreme sea, is synthesized. For investigating the consequences of specific extreme sea conditions this paper analyses extreme roll motions and the capsizing of a RO–RO vessel in a severe storm wave group. In addition, the seakeeping behaviour of a semi-submersible in the Draupner New Year Wave, embedded in extreme irregular seas is numerically and experimentally evaluated.