Vertical variations of coral reef drag forces

Modeling flow in a coral reef requires a closure model that links the local drag force to the local mean velocity. However, the spatial flow variations make it difficult to predict the distribution of the local drag. Here we report on vertical profiles of measured drag and velocity in a laboratory reef that was made of 81 Pocillopora Meandrina colony skeletons, densely arranged along a tilted flume. Two corals were CT-scanned, sliced horizontally, and printed using a 3-D printer. Drag was measured as a function of height above the bottom by connecting the slices to drag sensors. Profiles of velocity were measured in-between the coral branches and above the reef. Measured drag of whole colonies shows an excellent agreement with previous field and laboratory studies; however, these studies never showed how drag varies vertically. The vertical distribution of drag is reported as a function of flow rate and water level. When the water level is the same as the reef height, Reynolds stresses are negligible and the drag force per unit fluid mass is nearly constant. However, when the water depth is larger, Reynolds stress gradients become significant and drag increases with height. An excellent agreement was found between the drag calculated by a momentum budget and the measured drag of the individual printed slices. Finally, we propose a modified formulation of the drag coefficient that includes the normal dispersive stress term and results in reduced variations of the drag coefficient at the cost of introducing an additional coefficient.