Analysis of Ocean Waves by Crossing- and Oscillation-intensities

In this paper, relationships between wave characteristics and upcrossing-and oscillation-intensities are used to construct conservative bounds for signiicant wave heights and amplitudes and for moments of waves crests and troughs. A concept of oscillation ltering is introduced for removing small waves. Results are illustrated by ve examples in which both Gaussian and non-Gaussian models for a sea or a load are considered. BASIC DEFINITIONS AND RESULTS Let x(t) be the height of the sea level at a xed point as a function of time t. In oceanographic applications x(t) is often seen as a sequence of waves where each wave can be described by means of its highest and lowest values (crest, trough), or by means of its amplitude (= crest-trough) and wave period, describing the duration of a single wave. There is no general agreement about the formal deenition of a wave. Often one uses the so called mean downcrossing wave, where the wave is considered as a part of a function between the consecutive downcrossings of the mean sea level, (see the following deenition). Deenition 1 Assume x(t) crosses a xed reference level u-nitely many times, (here the level most frequently crossed by x). Denote by ti , 0 < t1 < t2 < : : : , the times of downcrossings of u. The trough and crest m i , M i , say, of the i th wave are the global minimum and the global maximum of x(t) , ti < t < ti+1 , respectively. The so called crest front amplitude H is deened as the diierence between the crest and the trough, i.e. t i <t<t i+1 x(t) ? min t i <t<t i+1 x(t): (1) (In the following the reference level u = 0 .) A simple measure of severity of waves are the signiicant wave amplitude and the signiicant crest height, denoted by H s , M s , averages of the highest one-third of amplitudes H i , crests heights M i , respectively. A more complete statistical characteristic of waves are (crest, trough)-and (wave period, amplitude)-distributions. Two major uses of wave characteristic distributions are to predict extreme waves and fatigue lifetimes of marine structures. Clearly, using the mean crossing waves one neglects small oscillations superimposed on major waves. However, for fatigue accumulation in marine structures, it is well known that even small oscillations can contribute to the damage and hence …