Palm distributions of wave characteristics in encountering seas

Details Palm distributions of wave characteristics in encountering seas Palm distributions of wave characteristics in encountering seas

2008-06-17

arxiv.org/abs/0806.2718v1

Annals of Applied Probability 2008, Vol. 18, No. 3, 1059-1084

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-AAP480 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/07-AAP480

Distributions of wave characteristics of ocean waves, such as wave slope, waveheight or wavelength, are an important tool in a variety of oceanographic applications such as safety of ocean structures or in the study of ship stability, as will be the focus in this paper. We derive Palm distributions of several wave characteristics that can be related to steepness of waves for two different cases, namely for waves observed along a line at a fixed time point and for waves encountering a ship sailing on the ocean. The relation between the distributions obtained in the two cases is also given physical interpretation in terms of a ``Doppler shift'' that is related to the velocity of the ship and the velocities of the individual waves.

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