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Slepian models for the stochastic shape of individual Lagrange sea waves

Lindgren, Georg LU orcid (2006) In Advances in Applied Probability 38(2). p.430-450
Abstract
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... (More)
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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Gaussian field, wave steepness, Slepian model, crossing theory
in
Advances in Applied Probability
volume
38
issue
2
pages
430 - 450
publisher
Applied Probability Trust
external identifiers
  • wos:000238756300007
  • scopus:33745933249
ISSN
0001-8678
DOI
10.1239/aap/1151337078
language
English
LU publication?
yes
id
1be3fdf4-1772-489b-bc98-9b156d8be4fc (old id 404697)
date added to LUP
2016-04-01 12:29:19
date last changed
2021-09-01 02:42:32
@article{1be3fdf4-1772-489b-bc98-9b156d8be4fc,
  abstract     = {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.},
  author       = {Lindgren, Georg},
  issn         = {0001-8678},
  language     = {eng},
  number       = {2},
  pages        = {430--450},
  publisher    = {Applied Probability Trust},
  series       = {Advances in Applied Probability},
  title        = {Slepian models for the stochastic shape of individual Lagrange sea waves},
  url          = {http://dx.doi.org/10.1239/aap/1151337078},
  doi          = {10.1239/aap/1151337078},
  volume       = {38},
  year         = {2006},
}