Momentum balance across a barrier reef Damien Sous, G. Dodet, F. Bouchette, M. Tissier To cite this version: Damien Sous, G. Dodet, F. Bouchette, M. Tissier. Momentum balance across a barrier reef. Journal of Geophysical Research. Oceans, Wiley-Blackwell, 2020, 125 (2), pp.e2019JC015503. 10.1029/2019JC015503. hal-02520270 HAL Id: hal-02520270 https://hal.archives-ouvertes.fr/hal-02520270 Submitted on 4 Aug 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. RESEARCH ARTICLE Momentum Balance Across a Barrier Reef 10.1029/2019JC015503 D. Sous1,2 , G. Dodet3 , F. Bouchette4,5 , and M. Tissier6 Key Points: 1 • The first complete evaluation of Mediterranean Institute of Oceanography (MIO), Université de Toulon, Aix Marseille Université, CNRS, IRD, La Garde, momentum balance over a reef France, 2Univ Pau & Pays Adour / E2S UPPA, Chaire HPC-Waves, Laboratoire des Sciences de lIngénieur Appliques a la barrier from measurements and Méchanique et au Génie Electrique Fédération IPRA, ANGLET, France, 3IFREMER, Univ. Brest, CNRS, IRD, Laboratoire numerical modeling d'Océanographie Physique et Spatiale (LOPS), IUEM, Brest, France, 4Geosciences-Montpellier, Univ Montpellier, • Reef hydrodynamics evolves from 5 6 classical beach regime on the forereef CNRS, Montpellier, France, GLADYS, Le Grau du Roi, Occitanie, France, Environmental Fluid Mechanics Section, to a friction-driven flow over the reef Faculty of Civil Engineering and Geosciences, Delft University of Technology, Stevinweg 1, Delft, The Netherlands flat • Wave resolving numerical simulations highlight the complexity Abstract This paper reports on a combined experimental and numerical study dedicated to barrier of the vertical structure of the flow reefs hydrodynamics. A network of pressure sensors and velocity profilers has been deployed for more than 2 months over the Ouano reef barrier, New Caledonia. The primary aim of the study is to assess the Correspondence to: relevance of the classical depth-averaged momentum balance in such a complex and poorly documented D. Sous, [email protected] environment. The combined analysis of experimental and numerical measurements reveals a specific hydrodynamic behavior contrasting with sandy beaches and fringing reefs. The cross-reef current induced by wave breaking over the barrier reef plays an important role in the momentum budget, in particular Citation: Sous, D., Dodet, G., Bouchette, F., & through friction processes. The hydrodynamic behavior over the barrier reef is thus characterized by the Tissier, M. (2020). Momentum progressive transition from a nearly classical beach type behavior on the forereef, where the gradient balance across a barrier reef. Journal of radiation stress is balanced by a barotropic pressure gradient associated to the wave setup, to an of Geophysical Research: Oceans, 125, e2019JC015503. https://doi.org/10. open-channel type regime, dominated by frictional head loss. The reef top wave setup shows a clear depth 1029/2019JC015503 dependency mainly attributed to the forereef curvature. During extreme wave events, the measurements tend to indicate a transition toward a critical hydraulic regime above the reef top. The numerical Received 19 JUL 2019 simulations, involving a non-hydrostatic wave-resolving model coupled to a K − turbulence model, Accepted 1 FEB 2020 highlight the vertical structure of the flow. Over the reef flat, a classical log-layer profile is observed, in Accepted article online 7 FEB 2020 agreement with measurements, while above the forereef an anticlockwise circulation develops under the breaking zone. 1. Introduction Coral reefs are facing a global degradation caused by ocean acidification and warming associated with increasing greenhouse gas emission and water pollution due to the growing anthropic pressure. Two major consequences of reef degradation are the increase of wave-driven flooding events (Storlazzi et al., 2015) and the deterioration of reef ecosystems and biological productivity. Improving the resilience of coral reefs is of primary importance for coral reef coasts in general and more particularly for small island develop- ing states that are vulnerable territories with often limited capacity for coastal mitigation solutions. The health of reef-lagoon ecosystems is directly dependent on the hydrodynamical functioning which controls the exchanges with the open ocean, the renewal of water masses, and the fluxes of nutrients, sediments, and contaminants. The hydrodynamics of nearshore systems are mainly governed by the coupling between wave action, water level, circulation and bottom friction. These processes are linked to each other within coupled wave-circulation numerical models through the depth-averaged momentum balance equation (Dodet et al., 2013; Roelvink et al., 2009). In coral reef environments, waves are often a major contributor to the momen- tum balance, affecting water level fluctuations and overall circulation within the lagoon or at the shore (Andréfouët et al., 2001; Angwenyi & Rydberg, 2005; Chevalier et al., 2014, 2015; Hench et al., 2008; Hoeke et al., 2013; Kench & McLean, 2004; Kraines et al., 1998, 1999; Lowe et al., 2009; Pomeroy et al., 2017; Sous et al., 2017; Taebi et al., 2011; Tartinville & Rancher, 2000; Wolanski et al., 1993). Recently, a diligent research effort has therefore been engaged to better understand wave transformation over coral reefs, in particular ©2020. American Geophysical Union. for fringing reefs (Gawehn et al., 2016; Monismith et al., 2013; Péquignet et al., 2011; Roeber & Cheung, All Rights Reserved. 2012; Van Dongeren et al., 2013; Vetter et al., 2010). SOUS ET AL. 1of24 Journal of Geophysical Research: Oceans 10.1029/2019JC015503 The present study aims to assess the depth-averaged momentum balance across barrier reefs. To better dis- criminate each of the processes involved, the simplest case of a purely cross-shore system under stationary wave forcing is discussed below. Under the assumption of steady flow and normally incident wave forcing averaged over many wave cycles, the depth-averaged alongshore uniform cross-shore momentum equation can be written as (Buckley et al., 2015; Gourlay & Colleter, 2005) ̄ 1 S 1 [ ] (U2)=−g − xx − ̄ Pa.m−1 , (1) x x (̄ + h) x (̄ + h) b where U is the depth-averaged velocity, g the gravitational acceleration, the water density, ̄ the wave setup, h the still water depth, Sxx the radiation stress, and b the bed shear stress. In the following, these four terms will be referred to as, from the left to the right in equation (1), the advection, slope, radiation, and friction terms. In fringing reef systems, the shore imposes theoretically a zero net depth-averaged trans- port across the reef. The depth-averaged momentum balance therefore reduces to the classical sandy beach form, although the friction term, due to waves and possibly to the offshore-directed near-bed mean veloc- ity (Buckley et al., 2016), plays a more prevailing role because of the generally high reef roughness. In their analysis of multiple fringing reefs, Vetter et al. (2010) and Becker et al. (2014) observed that the setup dis- plays a nearly linear dependency on incoming wave height with a maximal magnitude similar to the range observed on sandy beaches, that is, 15 − 20 % of the offshore wave height (Guza & Thornton, 1981). A number of analytical models derived from equation (1) with various degrees of simplification have been proposed and tested against field and laboratory data in reef contexts (Becker et al., 2014; Bonneton et al., 2007; Buckley et al., 2015, 2016; Gourlay & Colleter, 2005; Hearn, 1999; Massel & Gourlay, 2000; Monismith et al., 2013; Symonds et al., 1995; Vetter et al., 2010). A key characteristic of barrier reefs hydrodynamics, which are much less documented than fringing reef hydrodynamics, is that the gradient of radiation stress due to wave breaking induces a barotropic pressure gradient driving a net cross-shore current U across the barrier (Bonneton et al., 2007; Gourlay & Colleter, 2005; Hearn, 1999; Lowe et al., 2005; Lugo-Fernández et al., 1998; Monismith, 2007). This flow is expected to strongly affect the momentum balance by enhancing the friction term and, in the presence of strong bathymetric variations, the advection term. Extending the analysis on wave transformation over barrier reef carried out by Sous et al. (2019), the present study uses dedicated field measurements in order to investigate the depth-averaged momentum balance across barrier reefs. The approach builds on the observations of momentum dynamics carried out on coral reef systems (Hench et al., 2008; Lentz et al., 2016, 2017; Lowe et al., 2009; Monismith et al., 2013). The specific focus is here to quantify the spatial variations of each momentum flux term in equation (1) across a well-defined barrier reef and to examine the dependency of these terms on water level and wave forcing. In order to complete and extend the studied area, a series of numerical simulations is performed using a multilayer wave-resolving model. These numerical simulations