No abstract

No abstract

Extreme waves are studied in numerical simulations of the so-called Draupner seas that resemble the wave situation near the observation area of the Draupner wave, an iconic example of a freak, rogue wave. Recent new meteorological insights describe these seas as a substantial wind-generated wave system accompanied by two low-frequency lobes. With the significant wave height H s = 12 m above a depth of 70 m and the wide directional spreading over 120 • as design information, results are presented of simulations of phase resolved waves. Quantitative data are derived from 8000 waves over an area of 15 km 2 . Very high waves with crest heights exceeding 1.5 H s occur in average in 20 min timespan over an area of 0.8 km 2 . Details will be given for an isolated freak wave and a sequence of 3 freak crest heights in a group of 2 high waves. In Part 2, van Groesen and Wijaya (J Ocean Eng Mar Energy, 2017), it will be shown that 60 s before their appearance freak waves can be predicted from radar images on board of a ship that scans the surrounding area over a distance of 2 km.

To determine forces on fixed and flexible structures such as wind mills and oil platforms, experiments in wave tanks are useful to investigate the impacts in various types of environmental waves. In this paper we show that the use of an efficient simulation code can optimize the experiments by designing the influx such that waves will break at a predefined position of the structure. The consecutive actual measurements agree well with the numerical design of the experiments. Using the measured elevation close by the wave maker as input, the software recovers the experimental data in great detail, even for rather short (up to L/D=1) and very steep breaking waves with steepness parameter (ak) till 0.4. The experiments were carried out in the TUD-wavetank and the simulation is done by HaWaSSI-AB, a spatial-spectral implementation of a Hamiltonian Boussinesq model with an eddy-viscosity breaking mechanism that is initiated by a kinematic breaking condition.

No abstract

Numerical simulations are often used to predict the deformation of waves and their impact on structures in harbors and access channels. An underprediction of these waves could lead to structural failure or ship accidents, so accurate numerical models should be capable of capturing the complex physical processes correctly. In this contribution, the authors consider wave penetration into a harbor with a complex bathymetry from an access channel using numerical simulations with wave models in a software program. The wave models were derived based on consistent modeling using a variational principle for water waves to produce the dynamic equations in Hamiltonian form. By approximating the Hamiltonian, the so-called analytic Boussinesq (AB) model was used and discretized into a global spatial-spectral numerical method. Numerical results compared with laboratory experiments show better performance than in other publications on the same application.

SummaryWater waves propagating from the deep ocean to the coast show large changes in the profile, wave speed, wave length, wave height and direction. The fascinating processes of the physical wave phenomena give challenges in the study of water waves. The motion can exhibit qualitative differences at different scales such as deep water versus shallow water, long waves versus short waves. Therefore, the existing mathematical models are restricted to the limiting cases. This dissertation concerns the development of an accurate and efficient model that can simulate wave propagation in any range of wave lengths, in any water depth and moreover can deal with various inhomogeneous problems such as bathymetry and walls, leading to wave structure interactions.The derivation of the model is based on a variational principle of water waves. The resulting dynamic equations are of Hamiltonian form for wave elevation and surface potential with non-local operators applied to the canonical surface variables. The Hamiltonian is the total energy, i.e the sum of kinetic energy and potential energy. Since the kinetic energy cannot be expressed explicitly in the basic variables an approximation is required. The corresponding approximated Hamiltonian leads to approximated Hamilton equations.The approximate Hamilton equations are expressed in pseudo-differential operators applied to the surface variables. The pseudo-differential operator has a physical interpretation related to the phase velocity. The phase velocity as function of wave length is specified by a dispersion relation. Dispersion is one of the most important physical properties in the description of water waves. Accurate modelling of dispersion is essential to obtain high-quality wave propagation results.Using spatial-spectral methods and a straightforward numerical implementation, accurate and fast performance of the model can be obtained. Moreover, the spatialspectral implementation with the global pseudo-differential operators or a generalization with global Fourier integral operators (FIO) can retain the exact dispersion property of the model. Other numerical implementations with local differential operators such as finite difference or finite element methods require that the dispersion is approximated by an algebraic function. Such an approximation leads to restrictions on the range of wave lengths that are modelled correctly.To deal with practical applications, several extensions of the model are impleviii mented. The model with localization methods in the global FIO can deal with localized effects such as breaking waves, partially or fully reflective walls, submerged bars, run-up on shores, etc. The inclusion of a fixed-structure in the spatial-spectral setting is a challenging task. The method as presented here perhaps serves as a first contribution in this topic. An extended eddy viscosity breaking model and a breaking kinematic criterion are used for the wave breaking mechanism. The extended eddy viscosity breaking model can deal with fully dispersive waves. The...

No abstract