Markov Description of Wave-Crest Statistics

Abstract

Markov description of wave-crest statistics is considered for the case of severe random seas where Stokes nonlinearities require crests to rise higher than troughs fall. Of interest are the average number of consecutive high waves in runs of high waves and the average number of waves between beginnings of such runs, with high waves being defined in terms of a threshold level above mean water level. Two basic parameters are involved in the description: 1) the probability P that a high wave will occur at a fixed location, and 2) a coefficient C relating P to the probabilities associated with transitions from high to low waves and low to high waves. Comparison with laboratory measurements from scaled Bretschneider seas having a range of nonlinearities indicates that the basic Stokes nonlinearity is contained in the probability P , with no sensible dependence exhibited by the coefficient C . Additional comparison with scaled Jonswap seas illustrates the dependence of this coefficient on spectral shape. A final consideration of results from full-scale hurricane sea conditions, and from corresponding scaled laboratory data, demonstrates the general applicability of the laboratory results presented here to actual wind-driven seas.