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Fully Nonlinear Potential Flow Simulations of Wave Shoaling Over Slopes: Spilling Breaker Model and Integral Wave Properties

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Abstract

A spilling breaker model (SBM) is implemented in an existing two-dimensional (2D) numerical wave tank (NWT), based on fully nonlinear potential flow (FNPF) theory and the boundary element method (BEM), in which an absorbing surface pressure is specified over the crest of impending breaking waves (detected based on a maximum front slope criterion) to simulate the power dissipated during breaking. The latter is calibrated to match that of a hydraulic jump of parameters identical to local wave properties (height, celerity, \(\ldots \)). Although this model is not aimed at being fully physical in the surfzone, it allows more accurately simulating properties of fully nonlinear shoaling waves than standard empirical absorbing beaches (AB). After assessing the convergence with the discretization of 2D-NWT results for strongly nonlinear shoaling waves, simulations are first validated based on laboratory experiments for non-breaking and breaking waves, shoaling up a mild slope; a good agreement is found between both. The NWT is then used to compute fully nonlinear local (height, celerity, asymmetry) and integral (mean-water-level, radiation stress) properties of periodic waves shoaling over mild slopes. Discrepancies with standard results of wave theories are discussed in light of fully nonlinear effects modeled in the NWT. While only periodic waves are considered here, the SBM could be applied to shoaling irregular waves, for which the breaking point location will constantly vary, which would be advantageous compared to an AB fixed in space. For such cases, besides its more physical energy absorption, the SBM would allow better preventing wave overturning that may occur far from shore due to nonlinear wave–wave interactions and otherwise interrupt the FNPF–NWT simulations.

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Abbreviations

2D:

Two-dimensional

3D:

Three-dimensional

AB:

Absorbing beach

AP:

Absorbing piston wavemaker

BEM:

Boundary element method

BIE:

Boundary integral equation

BM:

Boussinesq model

BP:

Breaking point

FNPF:

Fully nonlinear potential flow

FSWT:

Fourier steady wave theory

LWT:

Linear wave theory

MII:

Middle interval interpolation

MWL:

Mean water level (wave-period averaged)

NWT:

Numerical wave tank

RMS:

Root mean square

SBM:

Spilling breaker model

SFW:

Stream function waves

VOF:

Volume of fluid

WM:

Wavemaker

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Acknowledgements

This research was supported by the US Office of Naval Research (ONR), initially under Grant N00014-99-1-0439 and, more recently Grants N00014-13-10687 and N00014-16-12970, from the US Department of the Navy, Office of the Chief of Naval Research. The information reported in this work does not necessarily reflect the position of the US Government.

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Authors and Affiliations

  1. Department of Ocean Engineering, University of Rhode Island, Narragansett, RI, 02882, USA

    Stephan T. Grilli

  2. Department of Ocean Engineering, Texas A&M University, Galveston, TX, USA

    Juan Horrillo

  3. Laboratoire IUSTI (UMR 7343), Aix Marseille Université, Technopôle de Château-Gombert 5 Rue Enrico Fermi, 13453, Marseille Cedex 13, France

    Stéphan Guignard

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Grilli, S.T., Horrillo, J. & Guignard, S. Fully Nonlinear Potential Flow Simulations of Wave Shoaling Over Slopes: Spilling Breaker Model and Integral Wave Properties. Water Waves 2, 263–297 (2020). https://doi.org/10.1007/s42286-019-00017-6

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