Elzbieta M. Bitner-Gregersen

Traditionally, wave parameters and their statistics has been derived from time series measurements of wave elevation. Recently, due to introduction in oceanography of stereo video camera systems, increasing attention has started to be given to spatial wave data and statistics. The present study is addressing temporal and spatial statistics of nonlinear waves giving focus to individual wave parameters. A directionally spread rogue-prone sea state observed in the North Sea is used as an example in the analysis which is based on numerical HOSM (Higher Order Spectral Method) simulations. The nonlinear order in the HOSM solver is set to M = 3, which includes the leading order nonlinear dynamical effects, including the effect of modulational instability. The following wave parameters are investigated: surface elevation, wave crests and wave troughs. The results demonstrate that the maximum spatial crest in a wave record can be up to 70% higher than the temporal crest. Further, the study indicates that the Gram-Charlier series can be used to fit the probability density function of surface elevation. It discusses applicability of the methodology based on the Gram-Charlier series for approximation of distributions of individual wave parameters of extreme and rogue waves and recommends further exploitation of this methodology. The results are discussed in the context of marine structures’ design.

Wave description is affected by several uncertainties, with sampling variability due to limited number of observations being one of them. Ideally, temporal/spatial wave registrations should be as large as possible to eliminate this uncertainty. This is difficult to reach in nature, where stationarity of sea states is an issue, but it can in principle be obtained in laboratory tests and numerical simulations, where initial wave conditions can be kept constant and intrinsic variability can be accounted for by changing random seeds for each run. Using linear, second-order, and third-order unidirectional numerical simulations, we compare temporal and spatial statistics of selected wave parameters and show how sampling variability affects their estimators. The JONSWAP spectrum with gamma peakedness parameters γ = 1, 3.3, and 6 is used in the analysis. The third-order wave data are simulated by a numerical solver based on the higher-order spectral method which includes the leading-order nonlinear dynamical effects. Field data support the analysis. We demonstrate that the nonlinear wave field including dynamical effects is more sensitive to sampling variability than the second-order and linear ones. Furthermore, we show that the mean values of temporal and spatial wave parameters can be equal if the number of simulations is sufficiently large. Consequences for design work are discussed.

The paper introduces a parameterization of the DNV GL storm profile for developing an analytical model for calculations of the return period of a storm whose peak exceeds a given threshold. The DNV GL storm evolution is represented via an isosceles trapezoidal shape in which the minor base represents the storm peak duration, the major base the total storm duration and the height is half of the highest significant wave height in the actual storm. In this representation, the storm duration is not related to the storm intensity and it is fixed constant and equal to 42 hours, while the peak duration is assumed to be 6 hours. The parameterization proposed in the paper consists in expressing the peak duration as a fraction of the total storm duration allowing to investigate the effects of storm peak duration on long term estimates. The analytical solution for the return period is derived by following the classical approach of Equivalent Storm Models that is referring to the equivalent storm sequence, with the only difference that all the Trapezoidal Storm durations are identical whatever the storm intensity is. This assumption leads to significant simplification on the model development and potential employment as well. Further, a closed form solution is achieved for the return period which is also a generalization of the triangular shape. Finally, data analysis with NDBC buoys data is carried out for validating the model and elucidating analogies and differences with respect to classical Equivalent Storm approach. Results have shown that the Trapezoidal Model can be thought as a triangular one with a prudential factor on the storm peak duration which results in a reasonable overestimation of maximum expected wave height and return values.

The 2012 guidelines on the method of calculation of the attained Energy Efficiency Design Index (EEDI) for new ships, MEPC.212(63), as updated by MEPC 245(66) in April 2014, represent a major step forward in implementing energy efficiency regulations for ships through the introduction of the EEDI limits for various types of ships. There are, however, serious concerns regarding the sufficiency of propulsion power and steering devices to maintain maneuverability of ships in adverse conditions, hence regarding the safety of ships, if the EEDI requirements are achieved by simply reducing the installed engine power. This was the rationale for a new EU funded research project with the acronym SHOPERA (2013-2016), aiming at developing suitable methods, tools and guidelines to effectively address the above concerns. The paper discusses the background of the ongoing research in project SHOPERA, presents early and intermediate results of the project and discusses certain fundamental issues regarding the formulation of proper criteria and practical assessment procedure for ship’s maneuverability and safety under adverse conditions.

Accuracy of an estimated design wave condition such as the 100-year significant wave height is important information for risk assessment in design of marine structures. Assessment of accuracy of design conditions is already not simple when they have been derived from in-situ wave measurements at the project site. When using wave hindcast data this task is even less straightforward due to often a lack of sufficiently reliable measurement data near the project site for comparison. Different hindcasts may give significant discrepancies in prediction of extremes. Also, the quality of the hindcast may vary over time. In practice, we often do not much more than illustrating the quality of the data, for example by scatter plots of hindcast data versus measurements far away from the project site. In order to assess the quality of a design wave height from a hindcast systematically, errors in both the local hindcast data and in the extrapolation from these data need to be addressed. The paper discusses the overall idea and some building blocks for such an approach, while realising that there will not be one simple recipe applicable in all situations. One of the issues is the selection and use of observational data in quality control. Satellite wave data are an attractive data source for this purpose. For illustration, data from the seas around Norway are used.