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Slope distribution in front-back asymmetric stochastic Lagrange time waves

Part of: Incompressible inviscid fluids Geophysics Waves Stochastic processes Geophysics (general)

Published online by Cambridge University Press:  01 July 2016

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

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The stochastic Lagrange wave model is a realistic alternative to the Gaussian linear wave model, which has been successfully used in ocean engineering for more than half a century. In this paper we present the slope distributions and other characteristic distributions at level crossings for asymmetric Lagrange time waves, i.e. what can be observed at a fixed measuring station, thereby extending results previously given for space waves. The distributions are given as expectations in a multivariate normal distribution, and they have to be evaluated by simulation or numerical integration. Interesting characteristic variables are the slope in time, the slope in space, and the vertical particle velocity when the waves are observed close to instances when the water level crosses a predetermined level. The theory has been made possible by recent generalizations of Rice's formula for the expected number of marked crossings in random fields.

Keywords

Crossing theoryGaussian processPalm distributionRice formulaSlepian modelwave steepness

MSC classification

Primary: 60G15: Gaussian processes
Secondary: 60G70: Extreme value theory; extremal processes 74J05: Linear waves 74J30: Nonlinear waves 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction 86A05: Hydrology, hydrography, oceanography
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 42 , Issue 2 , June 2010 , pp. 489 - 508
Copyright
Copyright © Applied Probability Trust 2010 

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