Data driven analysis on the extreme wave statistics over an area

Non-uniform bathymetry may modify the wave statistics for both surface elevation and velocity field. Laboratory evidence reported by Trulsen et al. (2012) shows that for a relatively long unidirectional waves propagating over a sloping bottom, from deep to shallower water, there can be a local maximum of kurtosis and skewness in surface elevation near the edge of the shallower side of the slope. Recent laboratory experiments of long-crested irregular waves propagating over a shoal by Trulsen et al. (2020) reported that the kurtosis of horizontal velocity field have different behaviour from the kurtosis of surface elevation where the local maximum of kurtosis in surface elevation and horizontal velocity occur at different location. In present work, we utilize numerical simulation to study the evolution of skewness and kurtosis for irregular waves propagating over a three-dimensional varying bathymetry. Numerical simulations are based on High Order Spectral Method (HOSM) for variable depth as described in Gouin et al. (2017) for wave evolution and Variational Boussinesq model (VBM) as described in Lawrence et al. (2021) for velocity field calculation.&#160;ReferencesGOUIN, M., DUCROZET, G. & FERRANT, P. 2017 Propagation of 3D nonlinear waves over an elliptical mound with a High-Order Spectral method. Eur. J. Mech. B Fluids 63, 9&#8211;24. LAWRENCE, C., GRAMSTAD, O. & TRULSEN, K. 2021 Variational Boussinesq model for kinematics calculation of surface gravity waves over bathymetry. Wave Motion 100, 102665. TRULSEN, K., RAUST&#216;L, A., JORDE, S. & RYE, L. 2020 Extreme wave statistics of long-crested irregular waves over a shoal. J. Fluid Mech. 882, R2. TRULSEN, K., ZENG, H. & GRAMSTAD, O. 2012 Laboratory evidence of freak waves provoked by non-uniform bathymetry. Phys. Fluids 24, 097101.

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A Note on the Extreme Wave Load and the Associated Probability of Failure

Journal of Ship Research ◽

10.5957/jsr.1986.30.2.123 ◽

1986 ◽

Vol 30 (02) ◽

pp. 123-126

Author(s):

A. E. Mansour

Keyword(s):

Probability Distribution ◽

Gaussian Process ◽

Random Process ◽

Narrow Band ◽

Spectral Width ◽

Probability Of Failure ◽

Stationary Random Process ◽

Wave Load ◽

Extreme Wave ◽

Wave Statistics

Introduction and background - The probability distribution of the peak process of a stationary random process with zero mean was first determined by Rice [1]. 2 Following his basic derivation, Longuet-Higgins [2] and Cartwright and Longuet-Higgins [3] evaluated various wave statistics, first for a narrow-band Gaussian process, then extended the results for a Gaussian process of any spectral width.

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Parametric Adjustments to the Rankine Vortex Wind Model for Gulf of Mexico Hurricanes

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.4006148 ◽

2012 ◽

Vol 134 (4) ◽

Cited By ~ 6

Author(s):

Chan Kwon Jeong ◽

Vijay Panchang ◽

Zeki Demirbilek

Keyword(s):

Gulf Of Mexico ◽

Extreme Wave ◽

Wind Fields ◽

Wind Model ◽

Rankine Vortex ◽

Wave Statistics ◽

Wind Speeds ◽

Vortex Model ◽

Hurricane Wind ◽

Adjustment Factors

Parametric wind models are often used to reconstruct hurricane wind fields from a limited set of hurricane parameters. Application of the Rankine Vortex and other models used in forecasting Gulf of Mexico hurricanes show considerable differences between the resulting wind speeds and data. The differences are used to guide the development of adjustment factors to improve the wind fields resulting from the Rankine Vortex model. The corrected model shows a significant improvement in the shape, size, and wind speed contours for 14 out of 17 hurricanes examined. The effect on wave fields resulting from the original and modified wind fields are on the order of 4 m, which is important for the estimation of extreme wave statistics.

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Extreme wave statistics of linear and nonlinear waves in Hurricane Camille

Maritime Technology and Engineering ◽

10.1201/b17494-145 ◽

2014 ◽

pp. 1353-1362

Keyword(s):

Nonlinear Waves ◽

Extreme Wave ◽

Wave Statistics ◽

Linear And Nonlinear Waves ◽

Linear And Nonlinear

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Extreme wave statistics of counter-propagating, irregular, long-crested sea states

Physics of Fluids ◽

10.1063/1.5034212 ◽

2018 ◽

Vol 30 (6) ◽

pp. 067102 ◽

Cited By ~ 4

Author(s):

Susanne Støle-Hentschel ◽

Karsten Trulsen ◽

Lisa Bæverfjord Rye ◽

Anne Raustøl

Keyword(s):

Extreme Wave ◽

Wave Statistics

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Comparison of linear and nonlinear extreme wave statistics

Acta Oceanologica Sinica ◽

10.1007/s13131-016-0862-5 ◽

2016 ◽

Vol 35 (5) ◽

pp. 99-105 ◽

Cited By ~ 2

Author(s):

Dmitry Chalikov ◽

Alexander V. Babanin

Keyword(s):

Extreme Wave ◽

Wave Statistics ◽

Linear And Nonlinear

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Joint statistical distribution of surface elevation and water velocity for irregular waves propagating over a shoal

10.5194/egusphere-egu2020-11732 ◽

2020 ◽

Author(s):

Karsten Trulsen

Keyword(s):

Local Maximum ◽

Mathematical Finance ◽

Water Velocity ◽

Statistical Distribution ◽

Surface Elevation ◽

Irregular Waves ◽

Extreme Wave ◽

Wave Statistics ◽

Finance Theory ◽

Multivariate Stochastic Process

In Trulsen et al. (2020) we reported that when irregular waves propagate over a shoal the extreme wave statistics of surface elevation and water velocity can be dramatically different: &#160;The surface elevation can have a local maximum of kurtosis some distance into the shallower part of the shoal, while it relaxes to normality after the shoal. &#160;The velocity field can have a local maximum of kurtosis after the shoal, while it is close to normality over the shallower part of the shoal. &#160;These two fields clearly do not coincide regarding the location of increased probability of extreme waves.Here we consider the evolution of the irregular waves over the shoal as a multivariate stochastic process, with a view to reveal the evolution of the joint statistical distribution of surface elevation and water velocity. &#160;Higher order multivariate moments, coskewness and cokurtosis, more commonly seen in mathematical finance theory, are employed to describe the joint extreme wave statistical distribution of the elevation and the velocity.Trulsen, K., Raust&#248;l, A., Jorde, S. & Rye, L. B. (2020) Extreme wave statistics of longcrested irregular waves over a shoal. &#160;J. Fluid Mech. 882, R2.

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