Hostname: page-component-5d59c44645-ndqjc Total loading time: 0 Render date: 2024-03-02T02:52:50.100Z Has data issue: false hasContentIssue false

Wave intensities and slopes in Lagrangian seas

Published online by Cambridge University Press:  01 July 2016

Sofia Åberg*
Lund University
Current address: Matematiska vetenskaper, Chalmers tekniska högskola, Göteborg SE-412 96, Sweden. Email address:
Rights & Permissions [Opens in a new window]


Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In many applications, such as remote sensing or wave slamming on ships and offshore structures, it is important to have a good model for wave slope. Today, most models are based on the assumption that the sea surface is well described by a Gaussian random field. However, since the Gaussian model does not capture several important features of real ocean waves, e.g. the asymmetry of crests and troughs, it may lead to unconservative safety estimates. An alternative is to use a stochastic Lagrangian wave model. Few studies have been carried out on the Lagrangian model; in particular, very little is known about its probabilistic properties. Therefore, in this paper we derive expressions for the level-crossing intensity of the Lagrangian sea surface, which has the interpretation of wave intensity, as well as the distribution of the wave slope at an arbitrary crossing. These results are then compared to the corresponding intensity and distribution of slope for the Gaussian model.

General Applied Probability
Copyright © Applied Probability Trust 2007 


Åberg, S., Rychlik, I. and Leadbetter, M. R. (2006). Palm distributions of wave characteristics in encountering seas. To appear in Ann. Appl. Prob. Google Scholar
Azaïs, J. M., León, J. R. and Ortega, J. (2005). Geometrical characteristics of Gaussian sea waves. J. Appl. Prob. 42, 407425.CrossRefGoogle Scholar
Baxevani, A., Podgórski, K. and Rychlik, I. (2003). Velocities for moving random surfaces. Prob. Eng. Mech. 18, 251271.CrossRefGoogle Scholar
Cramér, H. and Leadbetter, M. R. (1967). Stationary and Related Stochastic Processes. John Wiley, New York.Google Scholar
Fouques, S., Krogstad, H. E. and Myrhaug, D. (2006). A second order Lagrangian model for irregular ocean waves. Trans. AMSE J. Offshore Mech. Arctic Eng. 128, 177183.CrossRefGoogle Scholar
Gjøsund, S. H. (2003). A Lagrangian model for irregular waves and wave kinematics. Trans. AMSE J. Offshore Mech. Arctic Eng. 125, 94102.CrossRefGoogle Scholar
Lagrange, J. L. (1788). Mécanique Analytique. Jacques Gabay, Paris.Google Scholar
Leadbetter, M. R., Lindgren, G. and Rootzén, H. (1983). Extremes and Related Properties of Random Sequences and Processes. Springer, New York.CrossRefGoogle Scholar
Lindgren, G. (2006). Slepian models for the stochastic shape of individual Lagrange sea waves. Adv. Appl. Prob. 38, 430450.CrossRefGoogle Scholar
Lindgren, G. and Rychlik, I. (1991). Slepian models and regression approximation in crossings and extreme value theory. Internat. Statist. Rev. 59, 195225.CrossRefGoogle Scholar
Longuet-Higgins, M. S. (1957). The statistical analysis of a random, moving surface. Phil. Trans. R. Soc. London A 249, 321387.Google Scholar
Mercadier, C. (2006). Numerical bounds for the distributions of the maxima of some one- and two-parameter Gaussian processes. Adv. Appl. Prob. 38, 149170 CrossRefGoogle Scholar
Podgórski, K., Rychlik, I. and Machado, U. E. B. (2000). Exact distributions for apparent waves in irregular seas. Ocean Eng. 27, 9791016.CrossRefGoogle Scholar
Socquet-Juglard, H. et al. (2004). Spatial extremes, shapes of large waves, and Lagrangian models. In Proc. Rogue Waves (Brest, 2004). IFREMER, Plouzané. Available at Scholar
St. Denis, M. and Pierson, W. J. (1953). On the motion of ships in confused seas. Trans. Soc. Naval Architects Marine Eng. 61, 280357.Google Scholar