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The effects of smoothing length on the onset of wave breaking in smoothed particle hydrodynamics (SPH) simulations of highly directionally spread waves

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Abstract

Ocean wave breaking is a difficult-to-model oceanographic process, which has implications for extreme wave statistics, the dissipation of wave energy, and air–sea interaction. Numerical methods capable of reliably simulating real-world directionally spread breaking waves are useful for investigating the physics of wave breaking and for the design of offshore structures and floating bodies. Smoothed particle hydrodynamics is capable of modelling highly steep and overturning free surfaces, which makes it a promising method for simulating breaking waves. This paper investigates the effect of smoothing length on simulated wave breaking in both following and crossing seas. To do so, we reproduce numerically the experiments of highly directionally spread breaking waves in McAllister et al. (J Fluid Mech 860:767–786, 2019. https://doi.org/10.1017/jfm.2018.886) using a range of normalised smoothing lengths: \(h/d_p=1.4\), 1.7, 2.0, 2.3, with h smoothing length and \(d_p\) particle spacing. The smallest smoothing length we use appears to adversely affect the fidelity of the simulated surface elevation, so that the tallest wave crest observed in experiments is not fully reproduced (coefficient of determination \(r^2\approx 0.7\)). For smoothing lengths \(h/d_p=1.7\), 2.0, and 2.3, the experiments are well reproduced (\(r^2\ge 0.88\)); in these simulations smoothing length predominantly affects the spatial extent and duration of breaking. Qualitative and quantitative comparison of our simulations shows that values of \(h/d_p\) in the range \(1.7{-}2\) best reproduce the wave breaking phenomena observed in experiments.

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Acknowledgements

The authors acknowledge support from JSPS KAKENHI Grant Number 19J13966, 20K22396, and 20H02369. TSvdB acknowledges support from a Royal Academy of Engineering Research Fellowship.

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Authors and Affiliations

  1. Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima, Japan

    Taiga Kanehira, Takuji Nakashima & Hidemi Mutsuda

  2. Department of Engineering Science, University of Oxford, Oxford, OX1 3PJ, UK

    Mark L. McAllister

  3. Department of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester, M13 9PL, UK

    Samuel Draycott

  4. School of Engineering, University of Edinburgh, Edinburgh, EH9 3FB, UK

    David M. Ingram

  5. Department of Engineering Science, University of Oxford, Oxford, OX1 3PJ, UK

    Ton S. van den Bremer

  6. Faculty of Civil Engineering and Geosciences, Delft University of Technology, 2628 CD, Delft, The Netherlands

    Ton S. van den Bremer

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  1. Taiga Kanehira
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Kanehira, T., McAllister, M.L., Draycott, S. et al. The effects of smoothing length on the onset of wave breaking in smoothed particle hydrodynamics (SPH) simulations of highly directionally spread waves. Comp. Part. Mech. 9, 1031–1047 (2022). https://doi.org/10.1007/s40571-022-00463-z

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