How Consistent Are Estimates of Roughness Parameters on a Rough Coral Reef?

Abstract

Turbulent boundary layers, created by flws interacting with the rough topography of coral reefs, are important to many aspects of reef function and health (Davis et al., 2021). For example, turbulent boundary layers are important to coral health by supporting nutrient uptake (Lowe & Falter, 2015). For an unstratified, turbulent flow over a rough bottom, the boundary layer takes the form of the law-of-the-wall (Pope, 2012):where u(z) is the horizontal velocity at height z above the bed, u * is the friction velocity, z 0 is the roughness height, d is the displacement height, and we adopt the von Kármán constant κ = 0.41 following Nepf (2011). The friction velocity can also be calculated directly from the Reynolds stresses at the bed Abstract Coral reefs are hydrodynamically rough, creating turbulent boundary layers that transport and mix various scalars that impact reef processes and also can be used to monitor reef health. Often reef boundary layer characteristics derived from a single instrument are assumed to accurately represent the study site. This approach relies on two assumptions: first, that the boundary layer is relatively homogeneous across the area of interest, and second, that two instruments displaced in space or with different spatiotemporal resolution would produce similar results when sampling the same flow. We deployed four velocimeters over a 15 × 20 m reef at 10 m depth in the Chagos Archipelago. The site had a 1 m tidal range, and waves were primarily locally generated wind waves with H rms < 0.5 m. Depth-averaged currents were typically 0.2 m/s. Friction velocities derived directly from Reynolds stress measurements by fitting the law of the wall show agreement between instruments (pairwise coefficients of determination R 2 ranged from 0.53 to 0.86). Thus, the boundary layer appears to be spatially homogeneous, at least at the scale of our array, and it appears that in the present case friction velocities from one instrument are indeed generally representative of the site. We calculate drag coefficients using curve-fitting and Structure-from-Motion photogrammetry, and while we find general agreement between estimates one instrument in particular produces drag coefficients an order of magnitude larger in comparison. Hence, some variability between instruments was observed, notably when high-resolution instruments measured localized flow features.

Loss of reef roughness increases residence time on an idealized coral reef

“… and represent the smallest and largest drag coefficients observed on reefs, respectively. Estimated drag coefficients have been found to span orders of magnitude on real coral reefs 23 , 24 , e.g., in Moorea, French Polynesia 2 , in Chagos 25 , and 26 and 19 on different parts of the same reef system in Ofu, American Samoa. The results found by Refs.…”

“…To the author’s best knowledge, there is no widely accepted method of predicting drag coefficients a priori, although 19 proposed a geometry-based approach to evaluate that correlated well with hydrodynamically derived drag coefficients in both the original paper and in Ref. 25 . Adding to the complexity, Ref.…”