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A framework to quantify flow through coral reefs of varying coral cover and morphology [1]

['Andrew W. M. Pomeroy', 'Oceans Graduate School', 'The University Of Western Australia', 'Crawley', 'Western Australia', 'The Uwa Oceans Institute', 'Marco Ghisalberti', 'School Of Engineering', 'Michael Peterson', 'Vahid Etminan Farooji']

Date: 2023-03

Analytical framework for in-reef velocity

The analytical framework presented here builds on previous work by others, such as that by Lowe et al [33]. It predicts the ratio (β) of the horizontally- and depth-averaged in-reef velocity (U c , Fig 2) to the velocity well above the reef benthos (U ∞ ): (1) where ΔU is the difference between U ∞ and U c .

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TIFF original image Download: Fig 2. Conceptual model of the flow above and within benthos on a coral reef. For a given water depth (H), the near-surface flow velocity (U ∞ ) is greater than that within the reef region (U c ), which is defined by the height of the benthos (h) above the seabed. The plan area (A p ) and frontal area (A f ) are shown for the three archetypal coral forms in Fig 1 (“Table”, “Massive” and “Branching”). Note that Af is not simply the total coral area projected into the flow; rather, it is the sum of the projected areas of all coral surfaces. https://doi.org/10.1371/journal.pone.0279623.g002

The attenuation of the in-reef flow occurs due to the substantial drag forces imposed by coral reef colonies. For a given coral colony, this drag is typically described through a quadratic law relating the drag force (F D ) to the depth‐averaged in-reef flow velocity (U c ) and the area of the coral colony projected into the flow (the “frontal area” in Fig 2, A f ): (2) where ρ is the density of water, C D is a drag coefficient and ϕ is the porosity of the reef colony, which was calculated by treating the canopy as a box with the upper limit defined at the top of the coral morphology (z = h); the porosity is then equal to one minus the ratio of coral solid volume to box volume. We discuss the limitations of this approach to some morphologies such as plate corals later in the discussion. While complex forms such as branched corals (e.g., Pocillopora edyouxi) have been suggested to act as bluff bodies [34], A f is not simply the total coral area projected into the flow; rather, it is the sum of the projected areas of all coral surfaces (as all coral surfaces will exert drag and create flow attenuation). What this means is that, for example, for a branching coral each branch along the flow direction axis contributes to increase A f . We note this is not trivial for practical applications and we propose an approach to address this later. In this study, we evaluate the area projected into the incoming flow of each individual element (e.g., each individual branch) of each morphology and define A f as the sum of these projected areas.

When this is extrapolated to the reef scale, the drag force exerted per unit reef area and unit fluid density is: (3) where λ f (which is non-dimensional) is the total benthos frontal area per unit reef surface area. Below we show that λ f is a critically-important determinant of the in-reef flow. While evaluation of C D for a complex coral reef colony is not straightforward, measured values tend to lie in the range 0.5–2 [35–39]. Rather than try to quantify small changes in drag coefficient with coral and flow characteristics, we instead assume a constant value of C D = 1 for all coral morphologies. This assumption is borne out of practical necessity, as utilization of the framework presented here requires assumption of a coral drag coefficient value (which is otherwise not easily predicted). Later we discuss the implications of our choice and the need for a practical strategy to define C D , particularly for ‘non-front-facing’ morphologies.

For the case where the current is driven by a surface slope (e.g., tidal currents, wave breaking induced currents, etc.), conservation of momentum over the entire depth (H) and for a given water surface slope (S) requires a balance of the driving hydraulic gradient (left hand side of Eq 4) and the reef benthos drag (Eq 3, right hand side of Eq 4): (4) which can then be rearranged as: (5)

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[1] Url: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0279623

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