Comparison of Temporal and Spatial Statistics of Nonlinear Waves

2019 ◽  
Author(s):  
Elzbieta M. Bitner-Gregersen ◽  
Odin Gramstad
Keyword(s):  
Spatial Statistics ◽  
Modulational Instability ◽  
Rogue Waves ◽  
Nonlinear Dynamical ◽  
Wave Statistics ◽  
Wave Data ◽  
Camera Systems ◽  
Wave Parameters ◽  
Temporal And Spatial ◽  
Numerical Solver

Abstract In the past, it was most common to derive wave parameters and their statistics from time series of wave elevation. The duration of the wave records has been usually restricted to 20 or 30 minutes. Recently, increasing attention has started to be given to spatial wave data and wave statistics, particularly due to introduction in oceanography of stereo camera systems for collecting space–time ensemble of sea surface elevation. Using numerical linear, 2nd and 3rd order simulations this study compares temporal and spatial statistics of wave parameters. The 3rd order wave data are simulated by a numerical solver based on the Higher Order Spectral Method (HOSM) which includes the leading order nonlinear dynamical effects, accounting for the effect of modulational instability. The Pierson-Moskowitz and the JONSWAP spectrum with different gamma parameters are used in the analysis. Sea states with wave steepness where rogue waves were recorded in nature are considered. Consequences of using temporal contra spatial statistics are discussed in perspective of marine structures’ design. Functional dependency between wave parameters characterizing occurrence of rogue waves in unidirectional wave field is proposed.

Statistical Description of Nonlinear Waves

2021 ◽  
Author(s):  
Elzbieta M. Bitner-Gregersen ◽  
Odin Gramstad
Keyword(s):  
Nonlinear Waves ◽  
Modulational Instability ◽  
Video Camera ◽  
Rogue Waves ◽  
Surface Elevation ◽  
Nonlinear Dynamical ◽  
The North ◽  
Camera Systems ◽  
Wave Parameters ◽  
Individual Wave

Abstract 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.

scholarly journals Challenges in Description of Nonlinear Waves Due to Sampling Variability

2020 ◽  
Vol 8 (4) ◽  
pp. 279
Author(s):  
Elzbieta M. Bitner-Gregersen ◽  
Odin Gramstad ◽  
Anne Karin Magnusson ◽  
Mika Malila
Keyword(s):  
Numerical Simulations ◽  
Second Order ◽  
Intrinsic Variability ◽  
Third Order ◽  
Design Work ◽  
Sampling Variability ◽  
Mean Values ◽  
Wave Parameters ◽  
Temporal And Spatial ◽  
Numerical Solver

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.

Causal, temporal and spatial statistics of wildfires in areas of planted forests in Brazil

2019 ◽  
Vol 266-267 ◽  
pp. 157-172 ◽  
Author(s):  
Fernando Coelho Eugenio ◽  
Alexandre Rosa dos Santos ◽  
Beatriz Duguy Pedra ◽  
José Eduardo Macedo Pezzopane ◽  
Reginaldo Gonçalves Mafia ◽  
...  
Keyword(s):  
Spatial Statistics ◽  
Planted Forests ◽  
Temporal And Spatial

scholarly journals A preliminary investigation of rogue waves off the Jiangsu coast, China

2014 ◽  
Vol 14 (9) ◽  
pp. 2521-2527 ◽  
Author(s):  
Y. Wang ◽  
A.-F. Tao ◽  
J.-H. Zheng ◽  
D.-J. Doong ◽  
J. Fan ◽  
...  
Keyword(s):  
Coastal Area ◽  
Rogue Wave ◽  
Preliminary Investigation ◽  
Rogue Waves ◽  
Rayleigh Distribution ◽  
Wave Data ◽  
Open Questions ◽  
Wave Heights ◽  
New Type ◽  
Sea Area

Abstract. Due to the potential disasters induced by rogue waves, research in this field has increased rapidly in the last 2 decades. However, there are still a lot of open questions left, including some classic ones, such as whether the rogues waves are just rare events or not. One of the key reasons is that not enough of the observed rogue waves have been investigated. China has a wide sea area, but none of the research has addressed the observed rogue waves. In the present study, 1 year of observed wave data from Jiangsu coastal area, China, are analyzed. It is found that rogue waves are present, although the wave heights are not very large; furthermore, the probability of their occurrence is similar to the Rayleigh distribution prediction, due to the local silty coastal topography. The characteristics of rouge waves are investigated and the results indicate that a new type of rogue wave may exist.

Projected Changes in the Occurrence of Extreme and Rogue Waves in Future Climate in the North Atlantic

2017 ◽  
Author(s):  
Odin Gramstad ◽  
Elzbieta Bitner-Gregersen ◽  
Erik Vanem
Keyword(s):  
North Atlantic ◽  
Wave Spectrum ◽  
Wave Model ◽  
Rogue Waves ◽  
Wave Climate ◽  
Future Climate ◽  
The North ◽  
Wave Parameters ◽  
The Future ◽  
The North Atlantic

We investigate the future wave climate in the North Atlantic with respect to extreme events as well as on wave parameters that have previously not been considered in much details in the perspective of wave climate change, such as those associated with occurrence of rogue waves. A number of future wave projections is obtained by running the third generation wave model WAM with wind input derived from several global circulation models. In each case the wave model has been run for the 30-year historical period 1971–2000 and the future period 2071–2100 assuming the two different future climate scenarios RCP 4.5 and RCP 8.5. The wave model runs have been carried out by the Norwegian Meteorological Institute in Bergen, and the climate model result are taken from The Coupled Model Intercomparison Project phase 5 - CMIP5. In addition to the standard wave parameters such as significant wave height and peak period the wave model runs provided the full two-dimensional wave spectrum. This has enabled the study of a larger set of wave parameters. The focus of the present study is the projected future changes in occurrence of extreme sea states and extreme and rogue waves. The investigations are limited to parameters related to this in a few selected locations in the North Atlantic. Our results show that there are large uncertainties in many of the parameters considered in this study, and in many cases the different climate models and different model scenarios provide contradicting results with respect to the predicted change from past to future climate. There are, however, some situations for which a clearer tendency is observed.

Semiclassical relativistic fluid theory for electrostatic envelope modes in dense electron–positron–ion plasmas: Modulational instability and rogue waves

2013 ◽  
Vol 79 (6) ◽  
pp. 1089-1094 ◽  
Author(s):  
IOANNIS KOURAKIS ◽  
MICHAEL MC KERR ◽  
ATA UR-RAHMAN
Keyword(s):  
Fluid Model ◽  
Modulational Instability ◽  
Rogue Waves ◽  
Relativistic Electrons ◽  
Relativistic Fluid ◽  
Ion Plasma ◽  
Electron Positron ◽  
Electrons And Positrons ◽  
Perturbative Method ◽  
Fluid Theory

AbstractA fluid model is used to describe the propagation of envelope structures in an ion plasma under the influence of the action of weakly relativistic electrons and positrons. A multiscale perturbative method is used to derive a nonlinear Schrödinger equation for the envelope amplitude. Criteria for modulational instability, which occurs for small values of the carrier wavenumber (long carrier wavelengths), are derived. The occurrence of rogue waves is briefly discussed.

The Development of a New Global Atlas of Wave Statistics

1985 ◽  
Vol 38 (1) ◽  
pp. 145-149
Author(s):  
N. M. C. Dacunha ◽  
N. Hogben
Keyword(s):  
Ocean Wave ◽  
Wave Statistics ◽  
Wave Data ◽  
Preliminary Account ◽  
Previous Account ◽  
The Uk

In 1967 a compilation of visual wave data was published as a book with the title Ocean Wave Statistics, which is still widely used. In 1983 work began on the development of a new global atlas of wave statistics which will be available both as a book and as a computer database. This task is being undertaken by NMI Ltd in collaboration with the UK Meteorological Office with funding from the Department of Industry and is expected to take about three years. A preliminary account of the project has already been published. This article briefly recapitulates the case for the new atlas and updates the indication previously given of the proposed form of the contents, which has been revised in the light of comments received. Reference will be included to the plans for an associated database not mentioned in the previous account.

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