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On kurtosis and extreme waves in crossing directional seas: a laboratory experiment

Published online by Cambridge University Press:  08 August 2019

Jamie F. Luxmoore Open the ORCID record for Jamie F. Luxmoore [Opens in a new window] ,
Suzana Ilic Open the ORCID record for Suzana Ilic [Opens in a new window]  and
Nobuhito Mori Open the ORCID record for Nobuhito Mori [Opens in a new window]
Jamie F. Luxmoore
Affiliation:
College of Engineering, Mathematics and Physical Sciences, University of Exeter, Penryn Campus, Penryn, Cornwall TR10 9FE, UK
Suzana Ilic*
Affiliation:
Lancaster Environment Centre, Lancaster University, Lancaster LA1 4YQ, UK
Nobuhito Mori
Affiliation:
Disaster Prevention Research Institute, Kyoto University, Gokasho, Uji 611-0011, Japan
*
†Email address for correspondence: s.ilic@lancaster.ac.uk
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Abstract

We examine the statistical properties of extreme and rogue wave activity in crossing directional seas, to constrain the probabilistic distributions of wave heights and wave crests in complex sea states; such crossing seas alter the statistical structure of surface waves and are known to have been involved in several marine accidents. Further, we examine the relationship between the kurtosis as an indicator of nonlinearity in the spectrum and the directionality and crossing angles of the sea-state components. Experimental tests of two-component directionally spread irregular waves with varying frequency, directional spreading and component crossing angles were carried out at the Ocean Basin Laboratory in Trondheim, Norway. The results from the experiments show that wave heights are well described by a first-order (linear) statistical distribution, while for the wave crest heights several cases exceed a second-order distribution. The number of rogue waves is relatively low overall, which agrees with previous findings in directionally spread seas. The kurtosis and wave and crest height exceedance probabilities were more affected by varying the directional spreading of the components than by varying the crossing angles between components; reducing the component directional spreading increases the kurtosis and increases the exceedance probabilities. The kurtosis can be estimated quite well for two-component seas from the directional spreading using an empirical relationship based on the two-dimensional Benjamin–Feir index when the effects of bound modes are included. This result may allow forecasting of the probability of extreme waves from the directional spreading in complex sea states.

JFM classification

Waves/Free-surface Flows: Surface gravity waves

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JFM Papers
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Journal of Fluid Mechanics , Volume 876 , 10 October 2019 , pp. 792 - 817
Copyright
© 2019 Cambridge University Press 

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