Challenges in Description of Nonlinear Waves Due to Sampling Variability

Abstract

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.

Selected Papers from the Future Paths and Needs in Wave Modelling Workshop

“…For a proper understanding of extreme waves and crests, the latter reference also highlights the need to look for extremes over an area as well as over time, in which case "freak" wave observations may not be that freak anymore. This effect is also highlighted in the numerical study by Bitner-Gregersen et al [7].…”

“…This is important for engineering design, for which probabilistic methods are applied. A thorough numerical study on the variability in linear and nonlinear (second-order and third-order) wave records is caried out in [7]. Time-domain as well as spatial finite sampling are addressed.…”

“…As an outcome of the International Workshop "Future needs and challenges in wave modelling", held by SINTEF in Trondheim, Norway, 21-22 October 2019, this Special Issue includes 10 full Journal scientific papers [1][2][3][4][5][6][7][8][9][10] and two Technical notes [11,12], which have been prepared based on a selection of the Workshop presentations. All publications were peer-reviewed according to Journal standards by international experts.…”