Laboratory study on wave-induced setup and wave-driven current in a 2DH reef-lagoon-channel system
Introduction
A reef-lagoon-channel system is a typical reef configuration that can be found at barrier reefs or reef atolls. Ocean waves shoal on the steep fore-reef slope and then break around the reef edge, dissipating wave energy and producing a rise of mean sea level, namely “wave setup” as first described by Munk and Sargent (1948). The maximum setup usually occurs at the end of surf zone at outer reef flat, because on the inner reef flat the water level becomes almost constant, there is minimum forcing due to wave breaking. Differential wave-induced setup can drive a current across the shallow reef flat, through the deeper lagoon, and finally returning to the open sea through a rip channel, forming a two-dimensional horizontal (2DH) reef-lagoon-channel circulation cell (Lowe et al., 2009a). This kind of circulation is crucial to the transport, dispersal, and retention of coral larvae (e.g., Oprandi et al., 2019), nutrients (e.g., Falter et al., 2004), as well as sediments (e.g., Ouillon et al., 2010), thus it has important ecological and geological implications.
While a large amount of field observations (e.g., Hench et al., 2008; Lowe et al., 2009a; Monismith, 2014; Symonds et al., 2011; Taebi et al., 2011) and numerical simulations (Lowe et al., 2009b, 2010) have been reported in literatures for the waves and currents at natural reef sites, laboratory investigations of wave-induced setup and wave-driven current over coral reefs are fewer. Aside from the early studies (e.g., Gerritsen, 1980; Seelig, 1983), Gourlay (1996a) reported a full set of laboratory experiments using idealized physical reef models with an open/closed lagoon. Variations of the wave setup and mean current with both incident wave conditions and offshore water levels were analyzed. Subsequently, Demirbilek et al. (2007) designed a laboratory model based on the fringing reef profile of Seelig (1983) to investigate the combined effects of wind and waves on setup and run-up. Recently, Buckley et al. (2015) measured waves at spatially high-resolution in their wave flume to investigate the wave setup dynamics over a steeply sloping reef. They found that the surface roller effect in the surf zone is important via a theoretical analysis. The importance of a roller effect on surf zone wave-current dynamics has also been studied in Zheng et al. (2014). Buckley et al. (2016) extended their experiments to use artificial roughness elements on the same reef profile to reproduce the frictional effect. Yao et al. (2017) performed laboratory experiments to assess the impact of a reef crest located at the reef edge on the wave setup over an idealized fringing reef. More recently, Yao et al. (2018) experimentally investigated the wave-induced setup and wave-driven flow in a quasi-2DH reef-lagoon-channel system using a wave flume with a rip channel modeled by a pipe connecting the two ends of the flume. Their experiments were extended by Yao et al. (2019) to consider the presence of both shoreward and seaward directed tidal currents. Although, some of above studies attempted to model the 2DH reef-lagoon-channel configuration either by dividing a small wave basin into reef-channel sub-divisions (Gourlay, 1996a) or by using a pipe to simulate the rip channel in a wave flume (Yao et al., 2018), the alongshore variations of wave setup and current on the reef flat and in the lagoon could not be modeled due to the limits of their laboratory settings.
Laboratory studies of wave processes over a 2DH reef configuration are rare in the literature. To the authors’ knowledge, we are only aware that Smith et al. (2012) performed three-dimensional (3D) wave basin experiments to measure wave transformation, setup, and run-up over a fringing reef based on the bathymetry taken from a reef site in southeast Guam. They also conducted additional tests with an angled channel on the reef flat. However, their channel size was very small (0.15 m wide and 0.1 m deep) compared to the reef flat and there was no lagoon behind the reef flat, indicating that it was not a true reef-lagoon-channel system. Therefore, the hydrodynamics in a well-designed 2DH reef-lagoon-channel system needs to be further studied.
Over decades, in analogy to the radiation stress concept as introduced by Longuet-Higgins and Stewart (1964) to account for the mean wave and current dynamics on beaches, several 1DH models have been proposed to predict the wave setup and/or wave-driven current over reefs based on the conservation of momentum (Hearn, 1999; Symonds et al., 1995; Tait, 1972; Vetter et al., 2010; Yao et al., 2017) as well as the conservation of wave energy flux (Gourlay and Colleter, 2005). Lowe et al. (2009a) was the pioneering study to extend such approach to predict the wave setup and current in a reef-lagoon-channel system. Both momentum and mass balances were established in the reef surf zone, on the reef flat, as well as in the channel, respectively. Wave setup and mean current in the circulation cell can hence be solved when the bottom frictional and reef morphological features are known. Monismith (2014) employed a similar idea to develop his analytical solutions, but he focused on the cross-shore dynamics on the reef flat and alongshore dynamics in the lagoon instead. More recently, Yao et al. (2018) improved the model of Lowe et al. (2009a) by proposing an analytical solution for the cross-shore dynamics on the reef flat rather than solving the cross-shore momentum equation numerically. There is no requirement of a very small ratio of mean water level to reef-flat water level across the reef, which means Yao et al. (2018)'s model can also work for very low tidal level. Nevertheless, all above models are not fully 2DH in that they did not consider the hydrodynamic process either in the lagoon (Lowe et al., 2009a; Yao et al., 2018) or in the channel (Monismith, 2014).
Indeed, there is an analogy for the hydrodynamic pattern between the reef circulation and the rip current system on the barred sandy beaches or around the detached submerged breakwaters. For the latter, wave setup can also drive mean currents over the crests of bars or breakwaters, as well as the return currents directed to the open sea in the rip channels. There has been a wealth of studies in the literature to develop analytical or semi-analytical approaches for modeling waves and mean currents around such bars (e.g., Bellotti, 2004; Drønen et al., 2002; Moulton et al., 2017) and breakwaters (e.g., Calabrese et al., 2008; Zanuttigh et al., 2008). With regard to the reef-lagoon-channel system, however, we note that both the length scales and surface roughness of reef flat are significantly larger than those of a bar or a breakwater. This suggests that the wave energy decay/transfer due to both wave breaking and bottom friction across the wide reef flat, and the associated spatial variations of wave setup and currents may be more significant in the reef-lagoon-channel system.
Therefore, to remedy the lack of laboratory measurements of wave-induced setup and wave-driven current in a 2DH reef-lagoon-channel configuration in the literature, we report a new series of wave basin experiments to improve our current understanding in wave and circulation processes in a reef-lagoon-channel system. This physical model is designed based on field observation at Paopao Bay, Moorea, French Polynesia (Hench et al., 2008). In a well-controlled laboratory environment, the alongshore wave dynamics both on the reef flat and in the lagoon, as well as the extent and intensity of the circulation in the system can be assessed. We then extend the quasi-2DH analytical model as proposed by Yao et al. (2018) to fully 2DH dimension to reproduce our laboratory observation.
The rest of the article is organized as follows: the experimental settings are described in Section 2. Analyses of the wave-induced setup and wave-driven current data are described in Section 3. Model improvement and validation with the present experimental data is reported in Section 4. Major conclusions are drawn in Section 5.
Section snippets
Experimental setup
The laboratory experiments are performed to reproduce the main aspects of the wave dynamics in the reef-lagoon-channel system at Paopao Bay, Moorea, French Polynesia (Hench et al., 2008). This field system consists of two reefs (about 1 km wide) separated by a deep channel (an average of 300 m in alongshore width and 25 m in depth) as well as a deep lagoon (an average of 250 m in cross-shore width and 20 m in depth) behind the reefs (Fig. 1a). The cross-shore profile of the reef is
Wave height and mean water level (MWL) distributions in the reef-lagoon-channel system
Taking runs 2 and 11 ( or = 0.06 m, or = 2.0 s and = 0.04 m) as examples, wave gauge measurements enable us to construct the cross-reef wave height () and MWL () profiles along both the central cross-shore and alongshore transects (A-A′ and B–B’ in Fig. 2b) via a linear interpolation. The results are shown in Fig. 4, Fig. 5 for the regular and irregular waves, respectively. For regular waves, is calculated by the zero up-crossing method, while it is estimated as four times
An improvement on the model of Yao et al. (2018)
In this section, we extend the quasi-2DH semi-analytical model as proposed by Yao et al. (2018) to a fully 2DH framework to reproduce the present laboratory experiments. The original model considers a simplified reef-lagoon-channel circulation in which wave setup produced by breaking waves forces a current across the reef flat and exits from the channel. Following Yao et al. (2018), the cross-shore momentum balance as well as the mass balance based on the steady flow condition are established
Conclusions
To further investigate the wave-induced setup and wave-driven current in a 2DH reef-lagoon-channel system, a series of laboratory experiments have been carried out in a wave basin considering both regular and irregular waves. This idealized physical model is designed based on field observations, which allows us to examine the cross-shore and alongshore wave dynamics in the system. For the wave-induced setup and wave-driven current as focused in the present study, we found no notable difference
CRediT authorship contribution statement
Jinhai Zheng: Writing - review & editing, Supervision, Methodology, Funding acquisition. Yu Yao: Conceptualization, Methodology, Writing - original draft. Songgui Chen: Visualization, Resources, Project administration. Shubin Chen: Investigation. Qiming Zhang: Validation, Data curation.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This study was supported financially by the National Science Fund for Distinguished Young Scholars (Grant No. 51425901), the National Natural Science Foundation of China (Grant Nos. 51679014 and 51979013), the Scientific Research Fund of Hunan Provincial Education Department, China (Grant No. 18A116), Young Elite Scientist Sponsorship Program by the China Association for Science and Technology (Grant No. 2018QNRC001), Research Funds for the Central Universities (Grant No. TKS190201), and the
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