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Safety and Reliability

First Order Stochastic Lagrange Model for Asymmetric Ocean Waves

[+] Author and Article Information
Georg Lindgren1

Mathematical Statistics, Lund University, Lund SE-221 00, Swedengeorg@maths.lth.se

Sofia Åberg

Mathematical Statistics, Lund University, Lund SE-221 00, Sweden

1

Corresponding author.

J. Offshore Mech. Arct. Eng 131(3), 031602 (Jun 02, 2009) (8 pages) doi:10.1115/1.3124134 History: Received July 16, 2008; Revised February 02, 2009; Published June 02, 2009

The Gaussian linear wave model, which has been successfully used in ocean engineering for more than half a century, is well understood, and there exist both exact theory and efficient numerical algorithms for calculation of the statistical distribution of wave characteristics. It is well suited for moderate seastates and deep water conditions. One drawback, however, is its lack of realism under extreme or shallow water conditions, in particular, its symmetry. It produces waves, which are stochastically symmetric, both in the vertical and in the horizontal direction. From that point of view, the Lagrangian wave model, which describes the horizontal and vertical movements of individual water particles, is more realistic. Its stochastic properties are much less known and have not been studied until quite recently. This paper presents a version of the first order stochastic Lagrange model that is able to generate irregular waves with both crest-trough and front-back asymmetries.

FIGURES IN THIS ARTICLE
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Copyright © 2009 by American Society of Mechanical Engineers
Topics: Waves , Water
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Figures

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Figure 6

Cumulative distribution functions for slopes at upcrossings (solid lines) and negative slopes at downcrossings (dash-dotted lines) of levels −1, 0, 1, for linked Lagrange space waves with α=0.4 (smallest slope at level −1, largest at +1)

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Figure 4

Relation between the α-parameter and the degree of asymmetry. The solid line, A=0.319α, illustrates the fitted linear α to A relation, and dash-dotted curve is the α to log10 λAL relation.

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Figure 3

Average up- and downcrossing waves. Solid curves=crest-back profiles, centered at mean level upcrossings; dash-dotted curves=reversed crest-front profiles centered at downcrossings.

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Figure 2

Definition of asymmetry; space wave moving from left to right

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Figure 1

Linked Lagrange space waves with Pierson–Moskowitz orbital spectrum

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Figure 7

Similar to Fig. 6 but with α=0.8

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Figure 5

Cumulative distribution functions for slopes at upcrossings (and negative slopes at downcrossings) of levels −1, 0, 1, for front-back symmetric free Lagrange space waves with PM orbital spectrum with different peak periods Tp and different water depths (smallest slope at level −1 and largest at +1).

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