Simultaneous distributions for space-time wave characteristics in Gaussian sea

Eva Sjö

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2000

ISSN 1403-9338

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Abstract:

A simultaneous pair (L,T) is defined, representing wave length and period of the same wave.

For a homogeneous Gaussian spatio-temporal random sea model the simultaneous density for (L,T) is evaluated. The density is compared to the deterministic relation given by the dispersion relation, L=T²g/{pi}. A two-dimensional sea model, time and a single space coordinate, is used, based on a directional spectrum. Only the case of deep water is considered.

Furthermore, the wave height associated to the (L,T)-pair is studied. The (L,T)-distribution for significant waves is compared to ditto for all waves.

All results are compared to simulated observations, but no real data are considered.

Key words:

directional spectrum, Gaussian random field, Rice's formula, spatio-temporal waves, dispersion relation,

wave length, wave period