Abstract For the analysis of non-linear processes such as large rolling and capsizing of ships as well for the evaluation of forces and motion behavior of offshore structures in extreme sea states, experimental investigations are still indispensable, both for the validation of numerical sim- ulation tools and for basic insights into the underlying mechanism。 Especially in ship design numerical simu- lation tools have improved significantly and are already considered routinely within the design process but are still under development and require further experimen- tal confirmation。

One decisive point in such experimental investigations is the generation of deterministic wave sequences tailored for the inpidual test。 This requires modelling of the non-linear wave propagation in order to know the wave evolution in space and time which allows the analysis of the non-linear process as a cause-reaction chain。81331

In this paper methods of analyzing non-linear wave propagation are presented and compared to results of linear wave theory as well as to corresponding measure- ments from wave tank experiments。 A discussion of various practical applications closes the paper。

Keywords Non-linear wave propagation, deterministic wave trains, moving reference frame wave trains, RANSE/ VOF, nu- merical wave tank, wave generation, model tests, intact stability

Introduction The experimental investigation of extreme wave/structure interaction scenarios puts high de- mands on wave generation and calculation。 For the deterministic analysis of motions and forces of ships and offshore structures wave excitation denotes the beginning of a complex cause reaction chain。 The prob- lem gets complex when the structure which has to be analyzed is moving at constant or non-constant speed since measurements in a model tank cannot    provide

the wave train at the position of the investigated model or in the moving reference frame of a cruising ship。

This paper recommends the use of an approach tak- ing into account both analytical models and empirical terms for modelling non-linear wave propagation。 This modified non-linear method uses linear wave theory as a backbone for non-linear wave description and is de- veloped at each time step。 The main advantage of the proposed method is the representation, synthesis, and generation of an arbitrary wave train at any position in time and space。 Thus, standard model seas as well as special wave scenarios can be realized deterministically in a model tank and transformed either to other sta- tionary positions or to the moving reference frame of a cruising ship。

The above wave generation technique is used as a vali- dation tool for two numerical wave tanks。 The first nu- merical wave tank uses a time stepping method based on potential theory。 The simulation procedure calculates the free surface elevation and potential field of the entire fluid domain from which the pressure, velocity, and ac- celeration fields can be derived。 The second method is a commercial RANSE solver which solves the conserva- tion equations for mass and momentum。 For capturing the free surface the volume of fluid (VOF) approach is applied。 As a consequence, breaking phenomena can be considered。

A comparison with measurements discloses the advan- tages and disadvantages of each method。

The modified non-linear approach is applied to gener- ate the ”New Year Wave” which has been measured in the North Sea in the wave tank。 With this rogue wave sequence the motions and forces of a semisubmersible are  investigated experimentally。

The second application presented here addresses the ex- perimental investigation of intact stability。 The roll mo- tion of a RoRo vessel due to deterministic wave trains is given in the moving reference frame。 The test result is used for the practical design of ships by validating numerical tools for the evaluation of capsizing risk。