Two apparently distinct approaches to the analysis of wave groups in a random sea state are described. In the first, the probabilities of the group-length G and the length of a ‘high run’ H are defined in terms of a wave envelope function p (t) . These lead naturally to expressions in terms of a single parameter that defines the spectral width. In the second approach, the sequence of wave heights is treated as a Markov chain, with a non-zero correlation only between successive waves. This leads to expressions for G and H in terms of transition probabilities p + and p_. In this paper we find approximate analytic expressions for p + and p _ and that show that the two approaches are roughly equivalent, to order v . Throughout the paper it is emphasized that the concept of a wave group assumes implicitly the neglect of those harmonic components that are either very short or very long compared with the peak frequency o p . That is, some filtering of the original record is implied. For typical records of wind waves it is found that a band-pass filter with upper and lower cut-offs at 1.5 o p and 0.5 o p is the most suitable. Calculations are done for typical records of sea waves, and for some numerically simulated data, and there is agreement between the data and the analysis.

Statistical properties of wave groups in a random sea state

Chaos, fractals and self-organization in coastal geomorphology: simulating dune landscapes in vegetated environments

Analysis of freak wave measurements in the Sea of Japan

On-line wave prediction

This paper presents an analysis of a set of available freak wave measurements gatheredfrom several periods of continuous wave recordings made in the Sea of Japan during 1986–1990 by the Ship Research Institute of Japan. The analysis provides an ideal opportunity tocatch a glimpse of the statistics of freak waves in the ocean. The results show that a well-deﬁned freak wave may occur in the developed wind–wave condition: S(f) f 4 , with single-peak directional spectra. The crest and trough amplitude distributions of the observed seawaves including freak waves are different from the Rayleigh distribution, although the waveheight distribution tends to agree with the Rayleigh distribution. Freak waves can be readilyidentiﬁed from the wavelet spectrum where a strong energy density occurs in the spectrum,and is instantly surged and seemingly carried over to the high-frequency components at theinstant the freak wave occurs. 2002 Elsevier Science Ltd. All rights reserved. Keywords: Freak wave; Wave statistics; Wave height distribution; Wavelet analysis; Sea of Japan* Corresponding author. Tel.: +81-471-821-181; fax:+81-471-847-142.E-mail address:mori@criepi.denken.or.jp (N. Mori).

Technical Note Analysis of freak wave measurements in the Sea of Japan

This study deals with the statistical properties of the group formation of random waves determined by the zero-up-cross method. Probability distributions about (1) the run of high waves (2) the total run (3) the run of resonant wave period are derived theoretically providing that the time series of wave height and wave period form the Markov chain. Transition probabilities are given by the 2-dimensional Rayleigh distribution for the wave height train and the 2-dimensional Weibull distribution for the wave period train. And very good agreements between data and the theoretical distributions have been obtained. Then the paper discusses those parameters which affect the statistical properties of the runs and shows that the spectrum peakedness parameter for the. run of wave height and the spectrum width parameter for the run of wave period are the most predominant.

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Statistical properties of random wave groups

Wave height change of the zero-down-cross waves on uniform slopes were examined experimentally. The properties of shoaling, breaking and decay after breaking for a total of about 4,000 irregular waves of the Pierson-Moskowitz type on 4 different slopes (1/10, 1/20, 1/30 and 1/50) were investigated. The shoaling property of the zero-down-cross waves can be approximated by the linear wave theory. However, the properties of breaking and decay after breaking differ considerably from those for periodic waves. The wave height water depth ratio (H/d) at the breaking point for the zero-down-cross waves is about 30% smaller than that for periodic waves on average despite the slopes. Wave height decay after breaking also differs from that for periodic waves and can be classified into three regions, i.e. shoaling, plunging and bore regions. Experimental equations for the breaking condition and wave height change after breaking are proposed in the study. A new definition of water depth for the zero-crossing wave analysis which can reduce the fluctuation in the plotted data is also proposed.

/pdf/the-measured-properties-of-irregular-wave-breaking-and-wave-2x2o14na6q.pdf

The measured properties of irregular wave breaking and wave height change after breaking on the slope

The measurements of wave kinematics over the breakwater heads under uni and multidirectional waves attack were undertaken to achieve an improved understanding of the influence of wave directionality on the stability of heads. The characteristics of the magnitudes and directions of velocity vectors under 3D waves were assessed by comparing with those measured under 2D waves. The sensitive zones of the initial damage in the head sections were evaluated by linking the measurements of velocity components with a stability formula for armour stones on the heads, which was derived in this study.

https://icce-ojs-tamu.tdl.org/icce/index.php/icce/article/download/5342/5020

Velocity Field Measurements over Breakwater Heads under 3D Waves

A wave equation, taking account of the effects of porous medium, is transformed into coupled parabolic equations. It is assumed in the theory that the mean water depth and the thickness of porous layer are slowly varying and the bottom undulation is rapidly varying compared to the wavelength of surface waves. Though we can utilize the Bragg reflection to reduce transmitted waves behind breakwaters in one-dimensional case, wave heights behind breakwaters do not always decrease due to wave refraction-diffraction in horizontal two-dimensional case. By adding a dissipation term to the coupled parabolic equations, we can calculate the wave breaking deformation.

https://icce-ojs-tamu.tdl.org/icce/index.php/icce/article/download/5397/5073

Resonant Reflection and Refraction-Diffraction of Surface Waves due to Porous Submerged Breakwaters

https://icce-ojs-tamu.tdl.org/icce/index.php/icce/article/download/5272/4950

Akira Kimura

Papers

Statistical properties of random wave groups

The measured properties of irregular wave breaking and wave height change after breaking on the slope

Velocity Field Measurements over Breakwater Heads under 3D Waves

Resonant Reflection and Refraction-Diffraction of Surface Waves due to Porous Submerged Breakwaters

An attempt at applying the chaos theory to wave forecasting