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Numerical modeling of 3D fully nonlinear potential periodic waves

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Abstract

A simple and exact numerical scheme for long-term simulations of 3D potential fully nonlinear periodic gravity waves is suggested. The scheme is based on the surface-following nonorthogonal curvilinear coordinate system. Velocity potential is represented as a sum of analytical and nonlinear components. The Poisson equation for the nonlinear component of velocity potential is solved iteratively. Fourier transform method, the second-order accuracy approximation of vertical derivatives on a stretched vertical grid and the fourth-order Runge–Kutta time stepping are used. The scheme is validated by simulation of steep Stokes waves. A one-processor version of the model for PC allows us to simulate evolution of a wave field with thousands degrees of freedom for hundreds of wave periods. The scheme is designed for investigation of nonlinear 2D surface waves, generation of extreme waves, and direct calculations of nonlinear interactions.

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Notes

  1. Note that the term “linear” is conventional, since this component is also influenced by the nonlinearity due to curvature of the surface.

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Acknowledgments

The authors thank Dr. S. Suslov who made useful comments and Mrs. O. Chalikova for her assistance in preparation of the manuscript. The work was supported by RFBR, grant no. 11-05-0052 and Australian Research Council, Discovery grants DP1093349 and DP130100227.

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Authors and Affiliations

  1. Centre for Ocean Engineering, Science and Technology, Swinburne University of Technology, Hawthorn, Victoria, 3122, Australia

    Dmitry Chalikov, Alexander V. Babanin & Elena Sanina

  2. P.P. Shirshov Institute of Oceanology, 30, 1st Lane, V. I., Saint-Petersburg, 199053, Russia

    Dmitry Chalikov

Authors
  1. Dmitry Chalikov
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  2. Alexander V. Babanin
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  3. Elena Sanina
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Correspondence to Dmitry Chalikov.

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Responsible Editor: Oyvind Breivik

This article is part of the Topical Collection on the 13th International Workshop on Wave Hindcasting and Forecasting in Banff, Alberta, Canada October 27—November 1, 2013

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Chalikov, D., Babanin, A.V. & Sanina, E. Numerical modeling of 3D fully nonlinear potential periodic waves. Ocean Dynamics 64, 1469–1486 (2014). https://doi.org/10.1007/s10236-014-0755-0

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