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Slepian models for the stochastic shape of individual Lagrange sea waves

Part of: Geophysics (general) Geophysics Special processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Georg Lindgren
Georg Lindgren*
Affiliation:
Lund University
*
∗ Postal address: Department of Mathematical Statistics, Lund University, Box 118, SE-221 00 Lund, Sweden. Email address: [email protected]
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Abstract

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Gaussian wave models have been successfully used since the early 1950s to describe the development of random sea waves, particularly as input to dynamic simulation of the safety of ships and offshore structures. A drawback of the Gaussian model is that it produces stochastically symmetric waves, which is an unrealistic feature and can lead to unconservative safety estimates. The Gaussian model describes the height of the sea surface at each point as a function of time and space. The Lagrange wave model describes the horizontal and vertical movements of individual water particles as functions of time and original location. This model is physically based, and a stochastic version has recently been advocated as a realistic model for asymmetric water waves. Since the stochastic Lagrange model treats both the vertical and the horizontal movements as Gaussian processes, it can be analysed using methods from the Gaussian theory. In this paper we present an analysis of the stochastic properties of the first-order stochastic Lagrange waves model, both as functions of time and as functions of space. A Slepian model for the description of the random shape of individual waves is also presented and analysed.

Keywords

Slepian modelcrossing theorywave steepnessGaussian field

MSC classification

Primary: 60G60: Random fields
Secondary: 60G70: Extreme value theory; extremal processes 60K40: Other physical applications of random processes 86A05: Hydrology, hydrography, oceanography
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 38 , Issue 2 , June 2006 , pp. 430 - 450
Copyright
Copyright © Applied Probability Trust 2006 

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