Comparison of Dispersive and Nondispersive Models for Wave Run-Up on a Beach

A. Abdalazeez; I. I. Didenkulova; D. Dutykh; P. Denissenko

doi:10.1134/S0001433820050023

Comparison of Dispersive and Nondispersive Models for Wave Run-Up on a Beach

A. Abdalazeez
, I. I. Didenkulova
, D. Dutykh
, P. Denissenko

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Abstract: The applicability of dispersive and nondispersive wave models for describing long-wave propagation and run-up on a beach in the case of composite bottom topography is investigated: a plane beach transforms into a zone of constant depth. Numerical simulations are performed in the framework of two models: (1) nonlinear shallow-water theory and (2) the dispersive model in the Boussinesq approximation based on modified Peregrine equations. Simulations are compared with the data of a laboratory experiment for different types of waves: regular waves, biharmonic signals, and “vessel-like” wave trains strongly modulated by frequency and amplitude. Conclusions about the applicability of the corresponding theories for describing considered types of waves are drawn based on this comparison.

Original language	British English
Pages (from-to)	494-501
Number of pages	8
Journal	Izvestiya - Atmospheric and Ocean Physics
Volume	56
Issue number	5
DOIs	https://doi.org/10.1134/S0001433820050023
State	Published - 1 Sep 2020

Keywords

dispersive theory
frequency dispersion
modified Peregrine equations
nonlinear shallow-water theory
run-up of long waves on a coast
waves on the surface

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10.1134/S0001433820050023

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title = "Comparison of Dispersive and Nondispersive Models for Wave Run-Up on a Beach",

abstract = "Abstract: The applicability of dispersive and nondispersive wave models for describing long-wave propagation and run-up on a beach in the case of composite bottom topography is investigated: a plane beach transforms into a zone of constant depth. Numerical simulations are performed in the framework of two models: (1) nonlinear shallow-water theory and (2) the dispersive model in the Boussinesq approximation based on modified Peregrine equations. Simulations are compared with the data of a laboratory experiment for different types of waves: regular waves, biharmonic signals, and “vessel-like” wave trains strongly modulated by frequency and amplitude. Conclusions about the applicability of the corresponding theories for describing considered types of waves are drawn based on this comparison.",

keywords = "dispersive theory, frequency dispersion, modified Peregrine equations, nonlinear shallow-water theory, run-up of long waves on a coast, waves on the surface",

author = "A. Abdalazeez and Didenkulova, \{I. I.\} and D. Dutykh and P. Denissenko",

note = "Funding Information: Numerical simulations of frequency-modulated waves were performed with financial support from the Russian Science Foundation (grant no. 16-17-00041); other types of waves were simulated with support from the Russian Foundation for Basic Research (grant no. 18-05-80019) and grant PUT1378. Experimental data were collected as part of the Hydralab IV project, grant HyIV-FZK-03. We are also grateful to the PHC PARROT program, grant no. 37456YM, for supporting scientific visits to France and Estonia. Publisher Copyright: {\textcopyright} 2020, Pleiades Publishing, Ltd.",

year = "2020",

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doi = "10.1134/S0001433820050023",

language = "British English",

volume = "56",

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T1 - Comparison of Dispersive and Nondispersive Models for Wave Run-Up on a Beach

AU - Abdalazeez, A.

AU - Didenkulova, I. I.

AU - Dutykh, D.

AU - Denissenko, P.

N1 - Funding Information: Numerical simulations of frequency-modulated waves were performed with financial support from the Russian Science Foundation (grant no. 16-17-00041); other types of waves were simulated with support from the Russian Foundation for Basic Research (grant no. 18-05-80019) and grant PUT1378. Experimental data were collected as part of the Hydralab IV project, grant HyIV-FZK-03. We are also grateful to the PHC PARROT program, grant no. 37456YM, for supporting scientific visits to France and Estonia. Publisher Copyright: © 2020, Pleiades Publishing, Ltd.

PY - 2020/9/1

Y1 - 2020/9/1

N2 - Abstract: The applicability of dispersive and nondispersive wave models for describing long-wave propagation and run-up on a beach in the case of composite bottom topography is investigated: a plane beach transforms into a zone of constant depth. Numerical simulations are performed in the framework of two models: (1) nonlinear shallow-water theory and (2) the dispersive model in the Boussinesq approximation based on modified Peregrine equations. Simulations are compared with the data of a laboratory experiment for different types of waves: regular waves, biharmonic signals, and “vessel-like” wave trains strongly modulated by frequency and amplitude. Conclusions about the applicability of the corresponding theories for describing considered types of waves are drawn based on this comparison.

AB - Abstract: The applicability of dispersive and nondispersive wave models for describing long-wave propagation and run-up on a beach in the case of composite bottom topography is investigated: a plane beach transforms into a zone of constant depth. Numerical simulations are performed in the framework of two models: (1) nonlinear shallow-water theory and (2) the dispersive model in the Boussinesq approximation based on modified Peregrine equations. Simulations are compared with the data of a laboratory experiment for different types of waves: regular waves, biharmonic signals, and “vessel-like” wave trains strongly modulated by frequency and amplitude. Conclusions about the applicability of the corresponding theories for describing considered types of waves are drawn based on this comparison.

KW - dispersive theory

KW - frequency dispersion

KW - modified Peregrine equations

KW - nonlinear shallow-water theory

KW - run-up of long waves on a coast

KW - waves on the surface

UR - https://www.scopus.com/pages/publications/85094197171

U2 - 10.1134/S0001433820050023

DO - 10.1134/S0001433820050023

M3 - Article

AN - SCOPUS:85094197171

SN - 0001-4338

VL - 56

SP - 494

EP - 501

JO - Izvestiya - Atmospheric and Ocean Physics

JF - Izvestiya - Atmospheric and Ocean Physics

IS - 5

ER -

Comparison of Dispersive and Nondispersive Models for Wave Run-Up on a Beach

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