Chapter 8

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 x_{o}, y_{o}, the random surface elevation and the relevant velocity potential will be close to well-defined deterministic functions η_{1}¯, ϕ_{1}¯ in a neighborhood of x_{o}, y_{o}; and likewise, if a wave of given exceptionally large height occurs at some point x_{o}, y_{o}, the random surface elevation and the relevant velocity potential will be close to well-defined deterministic functions η_{2}¯, ϕ_{2}¯ in a neighborhood ...

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