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

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--type roughness, where k is the roughness height and 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.