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The Theory of Quasi-Determinism

The theorem of the sufficient condition for a wave crest with a given very large elevation and the theorems of the sufficient and the necessary conditions for a wave with a given very large height are proven. These theorems imply that: if a wave crest of given exceptionally large elevation occurs at some point xo, yo, the random surface elevation and the relevant velocity potential will be close to well-defined deterministic functions η1¯, ϕ1¯ in a neighborhood of xo, yo; and likewise, if a wave of given exceptionally large height occurs at some point xo, yo, the random surface elevation and the relevant velocity potential will be close to well-defined deterministic functions η2¯, ϕ2¯ in a neighborhood of xo, yo. To follow the proofs given in this chapter it is necessary to know the basic concepts of stationary Gaussian processes given in Sections 4.1 and 4.2.


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