Accelerated reproduction of 2-D periodic waves

Abstract

The paper describes the attempt to develop the accelerated method of simulation of 2-D surface waves with a use of 2-D model derived by simplifications of 3-D equations for potential periodic deep-water waves. The derivation is based on separation of velocity potential in surface-fitted coordinates into linear and non-linear components and analysis of exact Poisson equation for non-linear component of potential on a free surface. This equation contains both the first and second derivatives of velocity potential. The analysis of very accurate multiple solutions for velocity potential obtained with 3-D model shows that these variables are linearly connected to each other, what allows to obtain the 2-D equation for first derivative of potential (i.e., the vertical velocity on a surface), what gives the closed 2-D formulation for 3-D problem of 2-D waves. The connection between first and second variables is not precise; hence, the method as a whole cannot be exact. However, the 2-D model derived is able to reproduce different statistical characteristics of 2-D wave field with good accuracy. The most evident advantage of new model consists of absence of calculation of 3-D structure of velocity potential what increases a speed of calculations by about two orders.

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References

  1. Chalikov D (2016) Numerical modeling of sea waves (2016) Springer. https://doi.org/10.1007/978-3-319-32916-1, 330

  2. Chalikov D (2018) Numerical modeling of surface wave development under the action of wind. Ocean Sci 14:453–470. https://doi.org/10.5194/os-14-453-2018

    Article  Google Scholar 

  3. Chalikov D (2020) High-resolution numerical simulation of surface wave development under the action of wind. Ocean Wave Stud. https://doi.org/10.5772/intechopen.92262

  4. Chalikov D, Babanin AV, Sanina E (2014) Numerical modeling of three-dimensional fully nonlinear potential periodic waves. Ocean Dyn 64(10):1469–1486

    Article  Google Scholar 

  5. Ducrozet G, Bonnefoy F, Le Touzé D, Ferrant P (2016) HOS-ocean: open-source solver for nonlinear waves in open ocean based on high-order spectral method. Comput Phys Commun 203:245–254. https://doi.org/10.1016/j.cpc.2016.02.017

    Article  Google Scholar 

  6. Engsig-Karup A, Madsen M, Glimberg S (2012) A massively parallel GPU-accelerated mode for analysis of fully nonlinear free surface waves. Int J Numer Methods Fluids 70:20–36. https://doi.org/10.1002/fld.2675

    Article  Google Scholar 

  7. Grue J, Fructus D (2010) Model for fully nonlinear ocean wave simulations derived using Fourier inversion of integral equations in 3D. Advances in numerical simulation of nonlinear water waves: 1–42

  8. Hasselmann K, Barnett RP, Bouws et al (1973) Measurements of wind-wave growth and swell decay during the Joint Sea Wave Project (JONSWAP). Tsch Hydrogh Z Suppl A8(12):1–95

    Google Scholar 

  9. Sanina E (2015) Statistics of wave kinematics in random directional wave fields. Swinburne thesis collection. http://hdl.handle.net/1959.3/394825

  10. Thomas LH (1949) Elliptic problems in linear differential equations over a network. Columbia University, New York

    Google Scholar 

Download references

Acknowledgments

The author would like to thank Mrs. O. Chalikova for her assistance in the preparation of the manuscript. This research was performed in the framework of the state assignment of Russian Academy of Science (Theme No. 0149-2019-0015) supported in part 15 (Section 2) by RFBR (Project No. 18-05-01122).

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Correspondence to Dmitry Chalikov.

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The original online version of this article was revised due to a retrospective Open Access cancellation.

Responsible Editor: Amin Chabchoub

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Chalikov, D. Accelerated reproduction of 2-D periodic waves. Ocean Dynamics 71, 309–322 (2021). https://doi.org/10.1007/s10236-020-01435-8

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Keywords

  • Phase-resolving wave modeling
  • Reduction of 3-D wave problem to 2-D
  • Wave’s development
  • Wave spectrum
  • Wind input
  • Dissipation