Modeling flow in coral communities with and without waves: A synthesis of porous media and canopy flow approaches

Both canopy flow and porous media theories have been developed independent of one another to predict flow through submerged porous structures. These approaches are very similar, albeit with some key differences in how canopy resistance forces are parameterized. Canopy models provide a means of parameterizing the shear stresses that occur at the top of the canopy, whereas porous media models can often provide a simpler and more tractable way of parameterizing turbulent form drag based on simple morphological metrics and empirical relationships already in the hydrology literature. We developed a set of equations combining aspects of both models and applied this hybridized model to predict the flow structure within an experimental canopy formed by the branching coral Porites compressa, using model parameter values obtained from the literature. Results from the model predictions agreed well with direct measurements of flow speed and flow forces derived from particle image velocimetry under conditions of both unidirectional and wave-driven oscillatory flow. The flow structure within benthic boundary layers can have important consequences on the ecology of benthic organisms and in turn how these organisms affect the hydrodynamics occurring within their environment. Early boundary layer models of turbulent, unidirectional flow over solid walls describe three distinct regions: a viscous sublayer, a logarithmic layer, and an outer layer (Schlichting and Gersten 2000). This simple, universal model has been successful in describing turbulent flow over various naturally rough bottoms (Raupach et al. 1991). However, the roughness of many bottoms is large enough to be more accurately described as submerged ‘‘canopy flows’’ (Nepf and Vivoni 2000). The use of the term ‘‘canopy’’ reflects the similarity these flows have to atmospheric flows over terrestrial canopies (Finnigan 2000). What distinguishes canopy flow models most from conventional boundary layer models are that (1) they describe the flow within the roughness elements, and (2) they include an inflection point in the mean velocity profile that leads to the generation of instabilities that enhance turbulent exchange between the canopy and the overlying water column (Ackerman and Okubo 1993; Ghisalberti and Nepf 2002). For both terrestrial canopies and aquatic canopies where the water depth is much greater than the canopy height (i.e., unconfined flow conditions), the shear stress at the top of the canopy is the dominant force driving flow inside the canopy and is opposed by form drag exerted by the canopy elements (Raupach et al. 1991). This shear-driven transfer of momentum to the canopy interior becomes less important as the water depth becomes shallow with respect to the canopy height; in this case, the flow becomes confined, also termed ‘‘depth limited’’ (Nowell and Church 1979; Nepf and Vivoni 2000). For shallow flows (i.e., those approaching ‘‘emergent’’ conditions), the contribution of boundary layer shear becomes negligible since the primary momentum balance is instead between the external pressure gradient and form drag (Nepf and Vivoni 2000). This transition results in greater flow within the canopy than would otherwise occur under unconfined conditions (Wu et al. 1999; Mcdonald et al. 2006). Analogous to confined unidirectional canopy flow, the shear-driven transfer of momentum to the interior of a canopy also becomes less important when they are subjected to wave-driven oscillatory flow. Under typical wave conditions, pressure-driven flow accelerations are balanced mostly by the form drag and inertial forces 1 Corresponding author ([email protected]). Acknowledgments We thank Marlin Atkinson for helping to inspire this work and for providing the coral skeletons used in the experiments as well as thank Katie Fitzgibbons for assisting with the coral roughness and porosity measurements. Finally, the authors are grateful for the comments from the reviewers who helped improve both the content and the clarity of the paper. This research was supported by grant OCE-0117859 from the National Science Foundation. RJL acknowledges support from an Australian Research Council Discovery Project grant DP0770094. Limnol. Oceanogr., 53(6), 2008, 2668–2680 E 2008, by the American Society of Limnology and Oceanography, Inc.