Maximum Wave Height Distribution Research Articles

THE OCCURRENCE OF EXTREME WAVE HEIGHT IN A TWO-DIMENSIONAL RANDOM WAVEFIELD IN COASTAL AREA

As the water waves come to the coastal area, the variation in dispersion relation due to the spatial inhomogeneity brings about the deformation of the wave shape. With the local bathymetry effect, the propagation of the wave experiences a complicated evolution process, including the reflection, wave shoaling and breaking, etc. Considering the directional spreading effect and wave refraction becomes indispensable when it comes to a two-dimensional (2D) problem in the random wavefield. Mori et al. (2011) indicated that the distribution of maximum wave height in deep-water is decided by the directional dispersion. In this research, we aim to discuss the occurrence of maximum wave height in the 2D wave evolution in the coastal area. It helps to estimate better extreme events in the prevention work of coastal hazards. To simulate the 2D propagation, we develop a nonlinear model as an extension work of Lyu et al. (2021), which considers the high order harmonic interactions of irregular waves before the breaking in surf zone.

Freak wave in a two-dimensional directional wavefield with bottom topography change. Part 1. Normal incidence wave

In the propagation and evolution of sea waves, previous studies pointed out that the occurrence of the freak wave height is significantly related to the quasi-resonant four-wave interaction in the modulated waves. From numerical--experimental study over an uneven bottom, the nonlinear effect caused by the bathymetry change also contributes to the occurrence of extreme events in unidirectional waves. To comprehensively analyse the two-dimensional wavefield, this study develops an evolution model for a directional random wavefield based on the depth-modified nonlinear Schrödinger equation, which considers the nonlinear resonant interactions and the wave shoaling the shallow water. Through Monte Carlo simulation, we discuss the directional effect on the four-wave interaction in the wave train and the maximum wave height distribution from deep to shallow water with a slow varying slope. The numerical result indicates that the directional spreading has a dispersion effect on the freak wave height. In a shallow-water environment, this effect becomes weak, and the bottom topography change is the main influencing factor in the wave evolution.

Freak wave in high-order weakly nonlinear wave evolution with bottom topography change

In deep-water, quasi-resonant four-wave interaction gives rise to the occurrence probability of extreme wave height, which leads to freak wave as a natural disaster. As water wave enters shallow water, four-wave interaction becomes weak and wave shoaling makes this effect become complicated. This study conducts a Monte Carlo simulation in modified Nonlinear Schrödinger equation considering bottom topography change, and gives spatial evolution of high-order nonlinearity in wave train from statistical moment. The result indicates, slope angle plays an important role in a shallow water depth, and steep slope brings about a significant enhancement of extreme event in distribution of maximum wave height and surface elevation.

Assessment of statistical parameter uncertainty in the reliability analysis of jacket platforms

Statistical uncertainty is undoubtedly introduced in the estimation of parameters usually involved in the physical or probabilistic models employed for reliability analysis. Provided that such models parameters are uncertain, the probability of failure and the reliability index become uncertain variables as well. In this work, a general formulation is introduced to account for parameter uncertainties in the reliability analysis of jacket platforms under storm conditions. A point estimates method based on the Rosenblatt transformation is used to compute the statistics of the failure probability and the reliability index. It has the advantage that the estimating points and weights are readily defined. The effect of considering parameter uncertainties in the probability distribution of maximum wave height and the environmental load model was assessed. The relative influence of the different sources of parameter uncertainty and the implications of neglecting it were examined. Credible bounds of failure probability and coefficients of variation of the reliability index were evaluated as means of charactering uncertainty in their estimation. A decision problem regarding optimal probabilities of failure for structural design using a risk model is also analyzed, showing that depending on the coefficient of variation of the failure probability greater safety margins may be required.

Dispersion Effects on Tsunami Propagation in South China Sea

As the Manila Trench is becoming the most tsunami-hazardous, it is necessary to ascertain the wave height and arrival time in the South China Sea region through numerical simulation of tsunamis generated from potential earthquake source along the Manila subduction zone. The Okada model is employed to generate tsunami. The surface elevation and depth-averaged horizontal velocity at first 5 min, coming from the simulation of shallow water equations, are then interpolated in the weakly dispersive model (FUNWAVE) to calculate tsunami propagation and far-field impact. The characteristics of tsunami wave height distribution in South China Sea are analyzed for the assessment of tsunami hazard near coasts around South China Sea due to the hypothetical earthquakes with magnitude of [Formula: see text] and the worst case scenario ([Formula: see text]). The maximum wave height distribution computed by the Boussinesq equations is compared with that by the shallow water equations to investigate the dispersion effects on propagation of tsunami in South China Sea. It is found that the dispersion effects of the tsunami waves propagating in South China Sea are not significant if the earthquake magnitude is large enough.

Earthquake Scenario-Based Tsunami Wave Heights in the Eastern Mediterranean and Connected Seas

We identified a set of tsunami scenario input parameters in a 0.5° × 0.5° uniformly gridded area in the Eastern Mediterranean, Aegean (both for shallow- and intermediate-depth earthquakes) and Black Seas (only shallow earthquakes) and calculated tsunami scenarios using the SWAN-Joint Research Centre (SWAN-JRC) code (Mader 2004; Annunziato 2007) with 2-arcmin resolution bathymetry data for the range of 6.5—Mwmax with an Mw increment of 0.1 at each grid in order to realize a comprehensive analysis of tsunami wave heights from earthquakes originating in the region. We defined characteristic earthquake source parameters from a compiled set of sources such as existing moment tensor catalogues and various reference studies, together with the Mwmax assigned in the literature, where possible. Results from 2,415 scenarios show that in the Eastern Mediterranean and its connected seas (Aegean and Black Sea), shallow earthquakes with Mw ≥ 6.5 may result in coastal wave heights of 0.5 m, whereas the same wave height would be expected only from intermediate-depth earthquakes with Mw ≥ 7.0 . The distribution of maximum wave heights calculated indicate that tsunami wave heights up to 1 m could be expected in the northern Aegean, whereas in the Black Sea, Cyprus, Levantine coasts, northern Libya, eastern Sicily, southern Italy, and western Greece, up to 3-m wave height could be possible. Crete, the southern Aegean, and the area between northeast Libya and Alexandria (Egypt) is prone to maximum tsunami wave heights of >3 m. Considering that calculations are performed at a minimum bathymetry depth of 20 m, these wave heights may, according to Green’s Law, be amplified by a factor of 2 at the coastline. The study can provide a basis for detailed tsunami hazard studies in the region.

Numerical simulation of tsunami wave height distribution for Turkish Black Sea coast in nonlinear dynamic keyboard model of underwater seismic source

In frames of nonlinear shallow water equations taking into account dissipative effects and bottom friction a numerical simulation of a possible catastrophic tsunami in the Black Sea basin is performed. The computation was performed for seismic sources with various locations in the south-eastern and north-western parts of the Black Sea basin. The location of model sources was selected taking into account more seismoactive zones and proposed recurrence periods of tsunamis for a given region. A seismic source was constructed in frames of a keyboard model of the earthquake source taking into account possible temporal and velocity characteristics of seismic processes in a concrete source. Using a keyboard model of the source, both kinematic and dynamic models of earthquake sources were considered. The keyboard model of an earthquake source with different-time motions of keyboard blocks permits considering various scenarios of processes possible at earthquakes in seismic sources and estimating the influence of these processes on the distribution of maximum wave heights along the coast. Two scenarios for each seismic source were considered: a dynamical model, when the source is divided into keyboard blocks which are shifted in the vertical direction for different times and a single block moving according to certain laws describing unloading in the seismic source on the realization of an earthquake. For each of the scenarios considered, wave characteristics were obtained and a spectral analysis was performed which permits clearing the most dangerous places of the coast for moderate or strong tsunamigenic earthquakes.

Estimation of Maximum Wave Height of Observation Data and its Application to Freak Wave Prediction

A linear envelope assumption and quasi-resonant four-wave interactions for deep-water random waves may influence the statistical properties of deep-water surface gravity waves. As a consequence, the exceedance probability of wave height substantially deviates from the expected distribution obtained by assuming linear narrow banded spectrum waves. Here the occurrence probability of maximum wave heights is compared with ocean wave measurements during the yearsd 2001-2005 around Japan. The maximum wave height distribution and probability of occurrence of freak waves are compared with theoretical expectations and are adjusted by the measured data. The proposed distribution well predicts extreme waves in nonlinear random wave fields.

On the extreme statistics of long‐crested deep water waves: Theory and experiments

Quasi‐resonant four‐wave interactions may influence the statistical properties of deep water long‐crested surface gravity waves. As a consequence, the wave height exceedance probability can substantially deviate from the expected distribution obtained by assuming that waves are linear. Here the occurrence probability of extreme events recently derived by N. Mori and P. Janssen (2006) is compared with wave tank data, where strong departures from Gaussian behavior are observed. Experimental wave height, maximum wave height distribution, and probability of occurrence of freak waves are compared with theoretical expectations. The theory well predicts extreme waves in nonlinear wavefields.

A software complex for the numerical simulation of generation and propagation of tsunami waves in various marine areas from dynamic seismic sources

[1] A software complex is designed for the simulation of tsunami generation by a dynamic seismic source consisting of several vertically moving blocks of a preset configuration. The program interface allows the user to change the source kinematics of the blocks as a function of the seismic source under consideration. The software makes it possible to display the tsunami wave propagation in a water area (unconstrained by concrete conditions), perform its monitoring, interrupt and resume computations, depict the tsunami wave propagation front, display the distribution of maximum wave heights in a marine area, construct histograms of maximum wave heights along a coastline, and construct the velocity fields of particles in the traveling wave, wave front velocities, and mareograms at any given points of the area under consideration. Using the software capabilities, current data and their variation in time can be obtained at any point of the calculation domain, and all results (both final and intermediate) can be saved in the form of both numerical data and plots or diagrams.

Maximum Wave Height Distribution in a Sea State: Effects of Record Length and Spectral Peakedness

The probability distribution of the maximum wave height in a sea state is examined in terms of the spectral peakedness and the sea state duration. The study is based on the analysis of numerically simulated Gaussian wave records with given target spectra to fulfill the long duration and stationarity jointly required conditions, seldom found in nature. Results indicate a clear dependence of the probability distribution structure and location on the record length and the spectral shape.

From seismology to oceanography: Locating the sources of the Earth’s hum

The observation of continuously excited free oscillations of the Earth, in the absence of earthquakes, was first made by Japanese scientists in 1998. Since then, attention has focused on elucidating the physical mechanism responsible for them. The mechanism must be shallow, as fundamental modes appear to be preferentially excited and it shows seasonal variability. An array-based method has been developed to detect and locate sources of very long period surface wave energy, utilizing the dispersive properties of Rayleigh waves and data from two large aperture arrays of very long period seismometers, in California and in Japan. It is shown that, for each array, there is a well defined preferential direction, which is stable over one season but changes significantly from winter to summer. The fluctuations as a function of time of the maximum stack amplitudes are correlated across the two arrays and point to the northern Pacific Ocean in the northern hemisphere winter and the southern oceans in the summer, correlating with the distribution of maximum wave height. It is inferred that the background oscillations originate primarily in the oceans, and are caused by a non-linear coupling mechanism involving the atmosphere (winds), the oceans (infragravity waves) and the seafloor.

Occurrence probability of a freak wave in a nonlinear wave field

The Edgeworth’s form of a cumulative expansion of the probability density function (PDF) of surface elevation expands the maximum wave height distribution to predict the occurrence probability of freak waves. This study investigated the enhancement of the occurrence probability of freak waves due to the fourth order moment of surface elevation, kurtosis, change and found that the nonlinear effects on the occurrence probability of a freak wave linearly depends on kurtosis for a small number of waves N=250. The statistical theory was compared with field data, and freak waves sometimes appear when not expected by the Rayleigh theory, but they were predicted by the proposed theory.

Numerical Simulation of the Wave Pattern within a Harbor due to Ship Waves

A numerical simulation methodology to predict the wave pattern within a harbor due to ship waves is presented. It is based on the spectral decomposition of the solitary incident wave, assuming that non-linear effects are negligible, which is the usual case. Each component is transformed using Berkhoff's mild slope model. Superposition of the different solutions allows reconstruction of the wave temporal history, from which the maximum wave height at any point within the harbor can be obtained. An application of the proposed methodology to study the protection structure for the Argentine Yatch Club, located within Buenos Aires harbor, is presented. Details about the schematization and the necessary data are explained. The maximum wave height distribution for the projected structure and the original situation are compared. A variant of the project is proposed and analyzed, showing a significant extra attenuation of the maximum wave heights. This illustrates the utility of the methodology for design purposes.

Discussion of “ Distribution of Maximum Wave Height ” by Miguel A. Corniero, Miguel A. Losada, and Luis A. Giménez‐Curto (January, 1985, Vol. 111, No. 1)

Discussion of “ <i>Distribution of Maximum Wave Height</i> ” by Miguel A. Corniero, Miguel A. Losada, and Luis A. Giménez‐Curto (January, 1985, Vol. 111, No. 1)

Discussion of “ Distribution of Maximum Wave Height ” by Miguel A. Corniero, Miguel A. Losada, and Luis A. Giménez‐Curto (January, 1985, Vol. 111, No. 1)

Discussion of “ <i>Distribution of Maximum Wave Height</i> ” by Miguel A. Corniero, Miguel A. Losada, and Luis A. Giménez‐Curto (January, 1985, Vol. 111, No. 1)

Closure to “ Distribution of Maximum Wave Height ” by Miguel A. Corniero, Miguel A. Losada, and Luis A. Giménez‐Curto (January, 1985, Vol. 111, No. 1)

Closure to “ <i>Distribution of Maximum Wave Height</i> ” by Miguel A. Corniero, Miguel A. Losada, and Luis A. Giménez‐Curto (January, 1985, Vol. 111, No. 1)

ESTIMATION OF ALONGSHORE DISTRIBUTION OF TYPHOON-GENERATED MAXIMUM WAVE HEIGHT AROUND THE JAPANESE COAST BASED ON WAVE HINDCASTING

The purpose of this paper is to estimate alongshore distribution of maximum wave height around the Japanese coast generated by long-term typhoons through wave hindcasting based on a spectral wave prediction model. First, the applicability of the model to the evaluation of typhoon-generated waves is confirmed from the comparison between hindcasted results and wave data observed during many typhoons in recent years. Second, based on the wave hindcasting for 120 typhoons which attacked Japan in the past 50 years, alongshore distribution of maximum wave heights and their occurrence probability are estimated and compared with that of design wave heights of coastal structures. It is deduced that the design wave heights in the western district of Japan seem to be slightly small for probable maximum wave heights.

日本の過去の津波に関する2, 3の問題

From already published tsunami tables of author (1985, W), Iida (1984, I) and Rika-nenpyo (1986, R), we study three problems. Obtained results are follows.1. Comparison of tsunami tables.1) Number of data in I's table is about two of it in W, s and R, s ones.2) The tsunami sources adapted in only I, s table distribute on the coasts of Japan Sea, the inlands and coasts of southwestern Japan, and off southeastern coasts of Hokkaido and the Sanriku coast. Some data of I's table are doubt, because the tsunami sources situate on the inlands.2. Distribution of maximum wave heights.1) The eastern coast of Kii Peninsula is attacked five times by tsunami with the wave height of more than five meters.2) The Sanriku coast is attacked four times by tsunami with the wave height of more than twenty meters.3. Locality of the coast on tsunami propagation.The coefficient on propagation distance (log Δ) in equation calculating tsunami magnitude Mt is one for all coasts in Japan. However, it differs from one by calculating at many tidegage stations. The values are 0.62 in the Pacific coast of Hokkaido, 1.16 in Hakodate to Sanriku coast and 0.92 in the Pacific coast of sothwestern Japan.They will depend mainly on the difference of submarine deformation, such as the trench, the trough and the continental shelf.