Slepian models for the stochastic shape of individual Lagrange random waves
Centre for Mathematical Sciences
Lund Institute of Technology,
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.
Slepian model; crossing theory; wave steepness; Gaussian field