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Large Eddy Simulation Modeling of Tsunami-Like Solitary Wave Processes Over Fringing Reefs

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Large Eddy Simulation Modeling of Tsunami-Like Solitary Wave Processes Over Fringing Reefs Nat. Hazards Earth Syst. Sci., 19, 1281–1295, 2019 https://doi.org/10.5194/nhess-19-1281-2019 © Author(s) 2019. This work is distributed under the Creative Commons Attribution 4.0 License. Large eddy simulation modeling of tsunami-like solitary wave processes over fringing reefs Yu Yao1,4, Tiancheng He1, Zhengzhi Deng2, Long Chen1,3, and Huiqun Guo1 1School of Hydraulic Engineering, Changsha University of Science and Technology, Changsha, Hunan 410114, China 2Ocean College, Zhejiang University, Zhoushan, Zhejiang 316021, China 3Key Laboratory of Water-Sediment Sciences and Water Disaster Prevention of Hunan Province, Changsha 410114, China 4Key Laboratory of Coastal Disasters and Defense of Ministry of Education, Nanjing, Jiangsu 210098, China Correspondence: Zhengzhi Deng ([email protected]) Received: 10 December 2018 – Discussion started: 21 January 2019 Accepted: 10 June 2019 – Published: 28 June 2019 Abstract. Many low-lying tropical and subtropical reef- the beach, overtop or ruin the coastal structures, and inundate fringed coasts are vulnerable to inundation during tsunami the coastal towns and villages (Yao et al., 2015). Some tropic events. Hence accurate prediction of tsunami wave transfor- and subtropical coastal areas vulnerable to tsunami hazards mation and run-up over such reefs is a primary concern in the are surrounded by coral reefs, especially those in the Pacific coastal management of hazard mitigation. To overcome the and Indian oceans. Among various coral reefs, fringing reefs deficiencies of using depth-integrated models in modeling are the most common type. A typical cross-shore fringing tsunami-like solitary waves interacting with fringing reefs, reef profile can be characterized by a steep offshore fore-reef a three-dimensional (3-D) numerical wave tank based on the slope and an inshore shallow reef flat (Gourlay, 1996). There computational fluid dynamics (CFD) tool OpenFOAM® is is also possibly a reef crest lying at the reef edge (e.g., Hench developed in this study. The Navier–Stokes equations for et al., 2008) and/or a narrow shallow lagoon existing behind two-phase incompressible flow are solved, using the large the reef flat (e.g., Lowe et al., 2009a). Over decades, fringing eddy simulation (LES) method for turbulence closure and the reefs have been well known to be able to shelter low-lying volume-of-fluid (VOF) method for tracking the free surface. coastal areas from flood hazards associated with storms and The adopted model is firstly validated by two existing lab- high surf events (e.g., Cheriton et al. 2016; Lowe et al., 2005; oratory experiments with various wave conditions and reef Lugo-Fernandez et al., 1998; Péquignet et al., 2011; Young, configurations. The model is then applied to examine the im- 1989). However, after the 2004 Indian Ocean tsunami, the pacts of varying reef morphologies (fore-reef slope, back- positive role of coral reefs in mitigating the tsunami waves reef slope, lagoon width, reef-crest width) on the solitary has attracted the attention of scholars who conduct postdis- wave run-up. The current and vortex evolutions associated aster surveys (e.g., Chatenoux and Peduzzi, 2007; Ford et with the breaking solitary wave around both the reef crest al., 2014; Mcadoo et al., 2011). There is consensus among and the lagoon are also addressed via the numerical simula- the researchers that, in addition to the establishment of the tions. global tsunami warning system, the cultivation of coastal vegetation (mangrove forest, coral reef, etc.) is also one of the coastal defensive measures against the tsunami waves (e.g., Dahdouh-Guebas et al., 2006; Danielsen et al., 2005; 1 Introduction Mcadoo et al., 2011). Numerical models have been proven to be powerful tools to investigate tsunami wave interaction A tsunami is an extremely destructive natural disaster, which with the mangrove forests (e.g., Huang et al., 2011; Maza et can be generated by earthquakes, landslides, volcanic erup- al., 2015; Tang et al., 2013, and many others). Comparatively tions and meteorite impacts. Tsunami damage occurs mostly in the coastal areas where tsunami waves run up or run down Published by Copernicus Publications on behalf of the European Geosciences Union. 1282 Y. Yao et al.: LES modeling of tsunami-like solitary wave processes over fringing reefs speaking, their applications in modeling coral reefs subjected ticularly when there is a sharp reef crest located at the reef to tsunami waves are still very few. edge; (2) wave breaking could not be inherently captured by Over decades, modeling wave processes over reef profiles Boussinesq-type models – thus empirical breaking model or face several challenges such as steep fore-reef slope, com- special numerical treatment is usually needed; (3) Boussi- plex reef morphology and spatially varied surface rough- nesq models could not resolve the vertical flow structure as- ness. Local but strong turbulence due to wave breaking in sociated with the breaking waves due to the polynomial ap- the vicinity of the reef edge needs to be resolved. Among proximation to the vertical velocity profile. various approaches for modeling wave dynamics over reefs, To remedy the above deficiencies of using Boussinesq- two groups of models are the most pervasive. The first group type models to simulate the solitary processes (wave break- focuses on using the phase-averaged wave models and the ing, bore propagation and run-up) over the fringing reefs, we nonlinear shallow water equations to model the waves and develop a 3-D numerical wave tank based on the computa- the flows, respectively, in field reef environments, and typ- tional fluid dynamics (CFD) tool OpenFOAM® (Open Field ically the concept of radiation stress (Longuet-Higgins and Operation and Manipulation) in this study. OpenFOAM® is Stewart, 1964) or vortex force (Craik and Leibovich, 1976) a widely used open-source CFD code in the modern indus- is used to couple the waves and the flows (e.g., Douillet et try supporting two-phase incompressible flow (via its solver al., 2001; Kraines et al., 1998; Lowe et al., 2009b, 2010; interFoam). With appropriate treatment of wave generation Van Dongeren et al., 2013; Quataert et al., 2015). As for mod- and absorption, it has been proven to be a powerful and effi- eling tsunami waves at a field scale, we are only aware of cient tool for exploring complicated nearshore wave dynam- Kunkel et al.’s (2006) implementation of a nonlinear shallow ics (e.g., Higuera et al., 2013b). In this study, the Navier– water model to study the effects of wave forcing and reef Stokes equations for an incompressible fluid are solved. morphology variations on the wave run-up. However, their For the turbulence closure model, although large eddy numerical model was not verified by any field observations. simulation (LES) demands more computational resources The second group aims at using the computationally efficient than Reynolds-averaged Navier–Stokes (RANS) equations, and phase-resolving model based on the Boussinesq equa- it computes the large-scale unsteady motions explicitly. Im- tions. This depth-integrated modeling approach employs a portantly, it could provide more statistical information for the polynomial approximation to the vertical profile of velocity turbulence flows in which large-scale unsteadiness is signif- field, thereby reducing the dimensions of a three-dimensional icant (Pope, 2000). Thus the LES model is adopted by con- problem by one. It is able to account for both nonlinear and sidering that the breaking-wave-driven flow around the reef dispersive effects at intermediate water level. At a laboratory edge/crest is fast and highly unsteady. The free-surface mo- scale, Boussinesq models combined with some semiempir- tions are tracked by the widely used volume-of-fluid (VOF) ical breaking wave and bottom friction models have been method. proven to be able to simulate the motions of regular waves In this study, we first validate the adopted model by the (Skotner and Apelt, 1999; Yao et al., 2012), irregular waves laboratory experiments of Roeber (2010) as well as our pre- (Nwogu and Demirbilek, 2010; Yao et al., 2016, 2019) and vious experiments (Yao et al., 2018). The robustness of the infragravity waves (Su et al., 2015; Su and Ma, 2018) over present model in reproducing such solitary wave processes fringing reef profiles. as wave breaking near the reef edge/crest, turbulence bore The solitary wave has been employed in many labo- propagating on the reef flat and wave run-up on the back- ratory/numerical studies to model the leading wave of a reef beach is demonstrated. The model is then applied to in- tsunami. Compared to the aforementioned regular/irregular vestigate the impacts of varying reef morphologies (fore-reef waves, the numerical investigations of solitary wave inter- slope, back-reef slope, lagoon width, reef-crest width) on the action with the laboratory reef profile are much fewer. Roe- solitary wave run-up. The flow and vorticity fields associated ber and Cheung (2012) was the pioneer study to simulate with the breaking solitary wave around the reef crest and the the solitary wave transformation over a fringing reef us- lagoon are also analyzed by the model results. The rest of ing a Boussinesq model. Laboratory measurements of the this paper is organized as follows. The numerical model is cross-shore wave height and current across the reef as con- firstly described in Sect. 2. It is then validated by the labo- ducted by Roeber (2010) were reproduced by their model. ratory data from the literature as well as our data in Sect. 3. More recently, Yao et al. (2018) also validated a Boussi- What follows in Sect. 4 are the model applications for which nesq model based on their laboratory experiments to as- laboratory data are unavailable. The main conclusions drawn sess the impacts of reef morphologic variations (fore-reef from this study are given in Sect.
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