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Inertial energy dissipation in shallow-water breaking waves

Published online by Cambridge University Press:  11 March 2020

W. Mostert Open the ORCID record for W. Mostert [Opens in a new window]  and
L. Deike Open the ORCID record for L. Deike [Opens in a new window]
W. Mostert*
Affiliation:
Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
L. Deike*
Affiliation:
Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA Princeton Environmental Institute, Princeton University, Princeton, NJ 08544, USA
*
†Email addresses for correspondence: wmostert@princeton.edu, ldeike@princeton.edu
†Email addresses for correspondence: wmostert@princeton.edu, ldeike@princeton.edu
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Abstract

We present direct numerical simulations of breaking solitary waves in shallow water to quantify the energy dissipation during the active breaking time. We find that this dissipation can be predicted by an inertial model based on Taylor’s hypothesis as a function of the local wave height, depth and the beach slope. We obtain a relationship that gives the dissipation rate of a breaking wave on a shallow slope as a function of local breaking parameters. Next, we use empirical relations to relate the local wave parameters to the offshore conditions. This enables the energy dissipation to be predicted in terms of the initial conditions. We obtain good collapse of the numerical data with respect to the theoretical scaling.

JFM classification

Waves/Free-surface Flows: Wave breaking Geophysical and Geological Flows: Shallow water flows Geophysical and Geological Flows: Air/sea interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 890 , 10 May 2020 , A12
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Mostert and Dieke supplementary movie 1

Video of spilling breaker at α=2^∘,h_0/d_0 =0.15, coloured by vorticity content in the liquid phase, with effective resolution Δx=L_0/2^14. (See main document for definition of nomenclature.)
Download Mostert and Dieke supplementary movie 1(Video)
Video 2 MB

Mostert and Dieke supplementary movie 2

Video of plunging breaker at α=3^∘,h_0/d_0 =0.3, coloured by vorticity content in the liquid phase, with effective resolution Δx=L_0/2^14. (See main document for definition of nomenclature.)

Download Mostert and Dieke supplementary movie 2(Video)
Video 2.3 MB

Mostert and Dieke supplementary movie 3

Video of strong plunging breaker at α=4^∘,h_0/d_0 =0.4, coloured by vorticity content in the liquid phase, with effective resolution Δx=L_0/2^14. (See main document for definition of nomenclature.)

Download Mostert and Dieke supplementary movie 3(Video)
Video 2.7 MB

Mostert and Dieke supplementary movie 4

Video of collapsing breaker at α=6^∘,h_0/d_0 =0.5, coloured by vorticity content in the liquid phase, with effective resolution Δx=L_0/2^14. (See main document for definition of nomenclature.)

Download Mostert and Dieke supplementary movie 4(Video)
Video 1.8 MB

Mostert and Dieke supplementary movie 5

Video of surging breaker at α=7^∘,h_0/d_0 =0.3, coloured by vorticity content in the liquid phase, with effective resolution Δx=L_0/2^13. (See main document for definition of nomenclature.)

Download Mostert and Dieke supplementary movie 5(Video)
Video 1.5 MB