Connecting Flow over Complex Terrain to Hydrodynamic Roughness on a Coral Reef

TLDR

Flow over complex terrain generates bottom stress, drag, turbulence, and a boundary layer, yet the link between hydrodynamic roughness (z₀) and such terrain remains poorly understood. The study aims to connect hydrodynamic roughness to reef terrain by conducting field observations and fine‑scale bathymetry measurements on a shallow coral reef in Ofu, American Samoa. The authors model the reef as a superposition of wavy bedforms and predict z₀ from the root‑mean‑square depth and streamwise slope using a linear coefficient a₁, following established wavy‑bedform approaches. The validated centimeter‑scale nonhydrostatic model demonstrates that reef drag is governed by pressure‑driven form drag dependent only on relative depth and averaged slope, aligns with k–δ roughness scaling, shows local velocity profiles averaging a log layer, and requires a grid resolution 10–50 times the dominant hydrodynamic scale, indicating applicability to other complex terrains.

Abstract

Abstract Flow over complex terrain causes stress on the bottom leading to drag, turbulence, and formation of a boundary layer. But despite the importance of the hydrodynamic roughness scale z 0 in predicting flows and mixing, little is known about its connection to complex terrain. To address this gap, we conducted extensive field observations of flows and finescale measurements of bathymetry using fluid-lensing techniques over a shallow coral reef on Ofu, American Samoa. We developed a validated centimeter-scale nonhydrostatic hydrodynamic model of the reef, and the results for drag compare well with the observations. The total drag is caused by pressure differences creating form drag and is only a function of relative depth and spatially averaged streamwise slope, consistent with scaling for k – δ -type roughness, where k is the roughness height and δ is the boundary layer thickness. We approximate the complex reef surface as a superposition of wavy bedforms and present a simple method for predicting z 0 from the spatial root-mean-square of depth and streamwise slope of the bathymetric surface and a linear coefficient a 1 , similar to results from other studies on wavy bedforms. While the local velocity profiles vary widely, the horizontal average is consistent with a log-layer approximation. The model grid resolution required to accurately compute the form drag is O (10–50) times the dominant horizontal hydrodynamic scale, which is determined by a peak in the spectra of the streamwise slope. The approach taken in this study is likely applicable to other complex terrains and could be explored for other settings.