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Structures and Safety Reliability

Distribution of Wave Height Maxima in Storm Sea States

[+] Author and Article Information
Z. Cherneva, P. Petrova

Centre for Marine Technology and Engineering (CENTEC), Instituto Superior Técnico, Technical University of Lisbon, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal

C. Guedes Soares1

Centre for Marine Technology and Engineering (CENTEC), Instituto Superior Técnico, Technical University of Lisbon, Avenida Rovisco Pais, 1049-001 Lisboa, Portugalguedess@mar.ist.utl.pt

1

Corresponding author.

J. Offshore Mech. Arct. Eng 133(4), 041601 (Apr 11, 2011) (5 pages) doi:10.1115/1.4003391 History: Received May 17, 2009; Revised September 28, 2010; Published April 11, 2011; Online April 11, 2011

The effect of the coefficient of kurtosis, as a measure of third order nonlinearity, on the distribution of wave height maxima has been investigated. Measurements of the surface elevation during a storm at the North Alwyn platform in the North Sea have been used. The mean number of waves in the series is around 100. The maximum wave statistics have been compared with nonlinear theoretical distributions. It was found that the empirical probability densities of the maximum wave heights describe qualitatively the shift of the distribution modes toward higher values. The tendency for the peak of distribution to diminish with an increase in the coefficient of kurtosis up to 0.6 is also clearly seen. However, the empirical peak remains higher than the theoretically predicted one. The exceedance probability of the maximum wave heights was also estimated from the data and was compared with the theory. For the highest coefficients of kurtosis, estimated at nearly 0.6, the theoretical distribution approximates very well the empirical data. For lower coefficients of kurtosis, the theory tends to overestimate the exceedance probability of the maximum wave heights.

FIGURES IN THIS ARTICLE
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Copyright © 2011 by American Society of Mechanical Engineers
Topics: Waves , Storms , Seas
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Figures

Grahic Jump Location
Figure 1

Relationships between different wave parameters: (a) steepness ε versus the coefficient of skewness λ30, (b) steepness ε versus the coefficient of kurtosis λ40, (c) coefficients of kurtosis λ40 versus the coefficient of skewness λ30, and (d) parameter Λappr=2.23λ40−0.11 and the same parameter for narrow-band spectrum, Λ=8/3λ40, versus the coefficient of kurtosis λ40

Grahic Jump Location
Figure 2

Empirical probability density functions (squares) for different λ40 compared with the Rayleigh (dashed line) and MER (thick line) distributions: (a) λ40=−0.3, (b) λ40=0, (c) λ40=0.3, and (d) λ40=0.6

Grahic Jump Location
Figure 3

The ratios Hmax/Hs versus λ40 for N=100

Grahic Jump Location
Figure 4

Exceedance probability of the maximum waves measured in the North Sea in series of 100 waves (circles) and different λ40 compared with the Rayleigh (dashed line), GC (thin line), and MER (thick line) based distributions: (a) λ40=−0.3, (b) λ40=0, (c) λ40=0.3, and (d) λ40=0.6

Grahic Jump Location
Figure 5

Exceedance probability of the ratios Hmax/Hs for N=100 and different λ40

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