Spurs-and-grooves (SAG) are a common and impressive characteristic of shallow fore reef areas worldwide. Although the existence and geometrical properties of SAG are well-documented ever since the 50’s, the literature concerning specifically the hydrodynamics around them is sparse. This study provides a characterization of the 3D flow patterns found on SAG formations, and a sensitivity of that flow for a set of short wave and SAG geometry parameters, as well as for alongshore and long wave forcing. Its main interest is to provide scientists predictive capability of the flow conditions for a set of conditions commonly found on coral reef systems with SAG formations. Delft3D-FLOW coupled with SWAN/XBeach (3D phase-averaged) was applied to model schematic SAG formations. Shore-normal shoaling waves on top of SAG formations are shown to drive two circulations cells, the first in deeper waters with offshore spur and onshore groove depth-averaged velocities (offshore cell), and the second in shallower depths with offshore groove and onshore spur depth-averaged currents (onshore cell). In the offshore cell, the cross-shore velocity profile shows vertically monotonic currents - onshore to grooves and offshore to spurs -, except for the bottom, at which velocities are always onshore. In the onshore cell, the velocity profile shows offshore surface velocities and onshore bottom currents for both spur and groove, with resulting depth-averaged offshore groove and onshore spur velocities. The mechanism driving this flow results from the wave forcing being mostly balanced by pressure gradients both in the cross-shore and alongshore, and the mismatch between those is balanced by horizontal turbulent forces, that are higher in deeper waters, and friction, larger in shallower waters. Variations of this pattern are associated with changes in the velocity profile, that fundamentally depend on the wave, SAG geometry and alongshore forcing parameters. The waves are the main driving of the SAG flow, and as such wave parameters play a fundamental role in the SAG hydrodynamics. Wave heights are the most important parameter associated with the flow strength - higher waves induce significantly stronger circulation cells. When wave heights start breaking due to depth limitation, the SAG circulation cell is lost, and the velocity profile shape starts having onshore surface and undertow with maximum values at mid depth. Wave periods have moderate influence on the velocity values found on SAG circulation cells - higher wave periods induce slightly higher velocities. When the wave steepness reaches the breaking limit, the whitecapping results in changes of the velocity profile similarly to the case of depth-induced breaking waves. The role of varying wave directions and directional spreadings could not be accurately evaluated due to uncertainties related to the importance of refraction and diffraction using a phase-averaged model. An initial assessment of their importance with a model neglecting refraction, thus with unchangeable wave direction, was performed. Results showed that oblique waves result in alongshore transport systems, i.e., cross-shore currents become significantly lower than in the alongshore. In those cases, the SAG offshore cell is lost, and the onshore cell gets wider and stronger. The SAG geometry has a very important role associated with the resulting SAG hydrodynamics. Overall, the spur height, SAG wavelength and the SAG shape provide the biggest influence on the hydrodynamics. The spur heights have significantly influence in the strength of SAG circulation cells - higher spur heights are associated with stronger flows. The SAG wavelengths moderately influence the strength of the flow, with longer SAG wavelengths resulting in not much stronger SAG circulation cells. Shorter SAG wavelengths do not present the offshore SAG circulation cell, due to higher alongshore mixing of momentum that gives offshore spur and groove currents in that zone. The shape of the SAG formations is, together with the wave heights, the most important parameter influencing the strength of the flow. SAG formations with peak spur height located further onshore (Buttress type) have SAG circulation with higher velocities involved and the zonation of the SAG circulation cells changes accordingly, i.e., lower peak spur height depths have circulation cells shifted onshore, with widening of the offshore cell. The reef slope, without significant interference in the strength or velocity profile shape, also affects the zonation of SAG circulation cells, with steeper slopes providing wider SAG offshore circulation cells. The groove width, the differential roughness between spur and groove, and the reef flat widths were shown to have a minor role in the SAG hydrodynamics. The alongshore forcing leads to an alongshore transport system. The degree of the alongshore dominance is directionally proportional to the alongshore forcing. In the cross-shore direction, the onshore SAG circulation cell was persistent, while the offshore cell can be undermined with large alongshore forcing. Long waves were shown to result in negligible influence in the mean SAG hydrodynamics, associated with the low long wave forcing observed in the SAG zone. They are primarily more important as approaching and within the reef flat, and the water exchange between this and the SAG zones was concluded to have limited influence in the SAG flow. In terms of coral growth and health, bottom shear stresses were found to be systematically higher over spurs than grooves, resulting in a higher potential for coral development over them due to increasing water motion. Accordingly, sediment transport potential is higher over spurs, for which alongshore currents are higher than grooves, thus sediments would tend to drift towards the grooves, where they would more likely deposit due to lower shear stresses. The fact that SAG with distinct shapes - with significant different peak spur height depths - experience similar bottom shear stresses suggests the existence of a range of ideal hydrodynamics conditions for coral development.

中文翻译：

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在直槽形态上对三维流动进行建模

马刺和凹槽 (SAG) 是全球浅滩前礁区常见且令人印象深刻的特征。尽管自 50 年代以来，SAG 的存在和几何特性已经有了充分的记录，但关于它们周围的流体动力学的文献却很少。这项研究提供了在 SAG 地层上发现的 3D 流动模式的特征，以及该流动对一组短波和 SAG 几何参数以及沿岸和长波强迫的敏感性。它的主要兴趣是为科学家提供对具有 SAG 地层的珊瑚礁系统中常见的一组条件的流动条件的预测能力。Delft3D-FLOW 与 SWAN/XBeach（3D 相位平均）相结合，用于模拟示意性 SAG 地层。显示在 SAG 地层顶部的岸边正常浅滩波驱动两个环流单元，第一个在具有离岸支线和陆上凹槽深度平均速度（离岸单元）的较深水域中，第二个在具有离岸凹槽和陆上支路的较浅深度中深度平均电流（陆上电池）。在离岸单元中，跨岸速度剖面显示垂直单调流——陆上到凹槽和离岸到马刺——除了底部，底部的速度总是在岸上。在陆上单元中，速度剖面显示了支流和凹槽的离岸表面速度和陆上底流，由此产生了深度平均的离岸凹槽和陆上支流速度。驱动这种流动的机制是由于波浪力主要由跨岸和沿岸的压力梯度平衡，而两者之间的不匹配由水平湍流力平衡，水平湍流力在较深的水域中较高，摩擦力在较浅的水域中较大水域。这种模式的变化与速度剖面的变化有关，这从根本上取决于波浪、SAG 几何形状和沿岸强迫参数。波浪是 SAG 流动的主要驱动力，因此波浪参数在 SAG 流体动力学中起着重要作用。波高是与流动强度相关的最重要参数 - 更高的波浪会导致明显更强的循环细胞。当由于深度限制波高开始中断时，SAG 循环单元丢失，并且速度剖面形状开始具有陆上表面和底流，在中间深度具有最大值。波浪周期对在 SAG 循环单元上发现的速度值有中等影响 - 更高的波浪周期会导致稍高的速度。当波陡度达到破碎极限时，白顶会导致速度剖面的变化，类似于深度诱导的破碎波的情况。由于与使用相位平均模型的折射和衍射的重要性相关的不确定性，无法准确评估变化的波方向和定向传播的作用。使用忽略折射的模型对其重要性进行了初步评估，因此波浪方向不变。结果表明，斜波导致沿岸运输系统，即，跨岸水流明显低于沿岸。在这些情况下，SAG 离岸电池会丢失，而陆上电池会变得更宽更坚固。SAG 几何形状对产生的 SAG 流体动力学具有非常重要的作用。总体而言，突刺高度、SAG 波长和 SAG 形状对流体动力学的影响最大。支线高度对 SAG 循环单元的强度有显着影响 - 更高的支线高度与更强的流动相关。SAG 波长适度影响流动的强度，较长的 SAG 波长导致不强得多的 SAG 循环单元。更短的 SAG 波长不存在海上 SAG 环流单元，因为更高的近岸动量混合在该区域产生海上支流和凹槽流。SAG 地层的形状与波高一起是影响流动强度的最重要参数。具有峰值支流高度位于更远陆上的 SAG 地层（Buttress 型）具有涉及更高速度的 SAG 环流，并且 SAG 环流单元的分区相应地发生变化，即较低的峰支高度深度使环流单元向陆上移动，随着离岸单元的加宽. 礁坡对强度或速度剖面形状没有显着干扰，也会影响 SAG 环流单元的分带，陡峭的斜坡提供更宽的 SAG 近海环流单元。凹槽宽度、突刺和凹槽之间的差异粗糙度以及礁坪宽度在 SAG 流体动力学中的作用较小。沿岸强迫导致沿岸运输系统。沿岸优势的程度与沿岸强迫方向成正比。在跨岸方向上，陆上SAG环流单元是持续存在的，而海上单元可能会受到较大的沿岸强迫的破坏。研究表明，长波对平均 SAG 流体动力学的影响可以忽略不计，这与在 SAG 区观察到的低长波强迫有关。它们主要是在接近礁坪并在礁滩内更为重要，并且可以得出结论，该带与半凹陷带之间的水交换对半凹陷流的影响有限。在珊瑚生长和健康方面，发现底部剪切应力在马刺上系统地高于凹槽，由于水运动的增加，导致珊瑚在它们上面发展的潜力更大。相应地，支流上的沉积物运输潜力更高，因为沿岸流高于凹槽，因此沉积物会倾向于向凹槽漂移，由于较低的剪切应力，它们更可能沉积在凹槽中。具有不同形状的 SAG - 具有显着不同的尖峰高度深度 - 经历相似的底部剪切应力这一事实表明，存在一系列适合珊瑚发育的理想流体动力学条件。