Slepian models for the stochastic shape of individual Lagrange random waves

Georg Lindgren

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338
Gaussian wave models have been successfully used since the early fifties to describe the development of random sea waves, in 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 unrealistic and can lead to unconservative estimates 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 unsymmetric water waves. Since the stochastic Lagrange model treats both the vertical and the horizontal movements as Gaussian processes, it can be analysed with methods from the Gaussian theory. This paper presents an analysis of stochastic properties of the first order stochastic Lagrange waves model, both as time functions and as space functions. Slepian models for the random shape of individual waves are also derived.
Key words:
Slepian model; crossing theory; wave steepness; Gaussian field