Three-dimensional Flow Over Spur-and-Groove Morphology

Abstract

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.