A study of tsunami-like solitary wave transformation and run-up over fringing reefs

Abstract. The estimate of an individual wave run-up is especially important for tsunami warning and risk assessment, as it allows for evaluating the inundation area. Here, as a model of tsunamis, we use the long single wave of positive polarity. The period of such a wave is rather long, which makes it different from the famous Korteweg–de Vries soliton. This wave nonlinearly deforms during its propagation in the ocean, which results in a steep wave front formation. Situations in which waves approach the coast with a steep front are often observed during large tsunamis, e.g. the 2004 Indian Ocean and 2011 Tohoku tsunamis. Here we study the nonlinear deformation and run-up of long single waves of positive polarity in the conjoined water basin, which consists of the constant depth section and a plane beach. The work is performed numerically and analytically in the framework of the nonlinear shallow-water theory. Analytically, wave propagation along the constant depth section and its run up on a beach are considered independently without taking into account wave interaction with the toe of the bottom slope. The propagation along the bottom of constant depth is described by the Riemann wave, while the wave run-up on a plane beach is calculated using rigorous analytical solutions of the nonlinear shallow-water theory following the Carrier–Greenspan approach. Numerically, we use the finite-volume method with the second-order UNO2 reconstruction in space and the third-order Runge–Kutta scheme with locally adaptive time steps. During wave propagation along the constant depth section, the wave becomes asymmetric with a steep wave front. It is shown that the maximum run-up height depends on the front steepness of the incoming wave approaching the toe of the bottom slope. The corresponding formula for maximum run-up height, which takes into account the wave front steepness, is proposed.

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“…As already mentioned, during its propagation along the basin of constant depth h 0 , the wave transforms as a Riemann wave (Zahibo et al, 2008):…”

Section: Analytical Solutionmentioning

confidence: 97%

“…In the case of constant depth, the solution is described by the Riemann wave (Stoker, 1957). Its adaptation for the boundary problem can be found in Zahibo et al (2008). In the case of a plane beach, the corresponding solution was found by Carrier and Greenspan (1958).…”

Section: Analytical Solutionmentioning

confidence: 99%

Nonlinear deformation and run-up of single tsunami waves of positive polarity: numerical simulations and analytical predictions

Abdalazeez

Didenkulova

Dutykh

2019

Nat. Hazards Earth Syst. Sci.

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“…The deeper water depth in front of the fore-reef slope in the experiments is 0.413 m, in which case the water depth above reef flat is 0.03 m. Incident solitary wave height is from 0.05 to 0.07 m. All generated solitary wave in the physical experiments were breaking over the fore-reef slope and formed bore-propagation over the reef flat. The design of the fore-reef slope, water depth over the reef flat, reef flat width and backreef slope was based on the reported literatures (Quataert et al 2015;Yao et al 2018), following Froude similarity with a geometric scale factor of 1:100. Although actual tsunamis often appear as a combination of transient and nonperiodic waves, the solitary waves adopted in this study have been employed in many related studies as a benchmark in modelling the behaviours of tsunamis (e.g.…”

Section: Model Calibration and Validationmentioning

confidence: 99%

“…Skotner and Apelt 1999;Yao et al 2012;Zhang et al 2018), irregular (e.g. Nwogu andDemirbilek 2010;Yao et al 2016;Zhang et al 2018), and solitary (Yao et al 2018) wave processes over fringing reefs. Comparing to the other depth-integrated models based on nonlinear shallow equations, the Boussinesqtype models are reported better in predicting the wave processes in deeper water in front of the fore-reef slope because of retention of dispersive terms (Yao et al 2012(Yao et al , 2018.…”

Section: Introductionmentioning

confidence: 99%

“…Nwogu andDemirbilek 2010;Yao et al 2016;Zhang et al 2018), and solitary (Yao et al 2018) wave processes over fringing reefs. Comparing to the other depth-integrated models based on nonlinear shallow equations, the Boussinesqtype models are reported better in predicting the wave processes in deeper water in front of the fore-reef slope because of retention of dispersive terms (Yao et al 2012(Yao et al , 2018. Recently, considerable efforts have been devoted to developing shock-capturing Boussinesq models (Tonelli and Petti 2009;Roeber and Cheung 2012;Shi et al 2012;Fang et al 2013;Kazolea et al 2014), which use a hybrid method combining finitevolume and finite-difference schemes.…”

Section: Introductionmentioning

confidence: 99%

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The influence of climate change on tsunami-like solitary wave inundation over fringing reefs

Shao

Liu

Gao

et al. 2019

Journal of Integrative Environmental Sciences

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The protective capability of fringing reefs against tsunami hazards has been reported in numerous post-disaster surveys. It is believed that global warming is changing the water level over the reef flat and reef surface roughness by sea-level rise and coral bleaching. For a better understanding of the influence of climate change on tsunami hazards over fringing reefs, this study utilized a shockcapturing Boussinesq wave model, FUNWAVE-TVD, to simulate the tsunami-like solitary wave propagation and run-up over fringing reefs. Calibrated and validated by the newly obtained experimental data, the present model with shock-capturing scheme, in which only the ratio of wave height to water depth is used to trigger wave breaking, shows reasonable prediction of solitary wave transformation and run-up height over sharply varying reef bathymetry. Numerical experiments were then carried out to investigate the effects of sea-level rise and degrading of the reef surface roughness on the solitary wave inundation distance and fluid force distribution in the inundation zone. Numerical results clearly demonstrate how tsunami hazards change within the inundation zone in response to higher water levels and lower reef roughness and suggest climate change, especially sea-level rise, will significantly increase tsunami hazards in the low-lying areas of the reef-lined coasts. Presented results are discussed for the effects of sea-level rise and coral bleaching on the solitary wave process and implications to further improve the resilience under the threat of climate change. ARTICLE HISTORY

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Numerical investigation of the hydrodynamic response of an impermeable sea-wall subjected to artificial submarine landslide-induced tsunamis

Deng

Cao

et al. 2021

Landslides

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Landslide-induced tsunamis are common natural hazards that potentially affect the safety and stability of waterfront structures. A numerical tank was constructed using FLOW-3D to investigate the hydrodynamic response of the sea-wall subjected to artificial submarine landslide-induced tsunamis, including the hydrodynamic load and wave run-up height. Initially, the landslideinduced tsunami model was calibrated using experiments to ensure high accuracy for capturing the free surface and obtaining the flow field information. Then, the sea-wall was added into the numerical tank to study the hydrodynamic response of the sea-wall. The results show that the artificial landslide successively generated two wave crests and that the hydrodynamic response of the seawall under the second crest was stronger than that under the first crest. Additionally, the effects of different influencing factors on the hydrodynamic response were discussed, respectively, and prediction equations for the hydrodynamic response considering these factors were proposed.

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A study of tsunami-like solitary wave transformation and run-up over fringing reefs

Cited by 55 publications

References 49 publications

Nonlinear deformation and run-up of single tsunami waves of positive polarity: numerical simulations and analytical predictions

Nonlinear deformation and run-up of single tsunami waves of positive polarity: numerical simulations and analytical predictions

The influence of climate change on tsunami-like solitary wave inundation over fringing reefs

Numerical investigation of the hydrodynamic response of an impermeable sea-wall subjected to artificial submarine landslide-induced tsunamis

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