On Markov Theory and Wave-Crest Statistics

Abstract

The Longuet-Higgins connection between Markov description of runs of high waves and the truncated frequency spectrum of a given sea is developed in a simplified, experimentally based manner using combined results from envelope and Markov theories. A high-frequency truncation limit is proposed as 2ωp – 0.5ωo , where ωp denotes peak spectral frequency and ωo denotes mean frequency. Results are shown to apply to measurements from laboratory and computer simulations of standard Bretschneider and Jonswap seas.