Flow inside a coral colony measured using magnetic resonance velocimetry

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1 Limnol. Oceanogr., 54(5), 2009, E 2009, by the American Society of Limnology and Oceanography, Inc. Flow inside a coral colony measured using magnetic resonance velocimetry Sandy Chang, a,* Chris Elkins, b Marcus Alley, c John Eaton, b and Stephen Monismith a a Department of Civil and Environmental Engineering, Stanford University, California b Department of Mechanical Engineering, Stanford University, California c Department of Radiology, Stanford University, California Abstract The velocity field within scale models of branching coral Stylophora pistillata colonies was measured using magnetic resonance velocimetry (MRV). The models were based on digital representations of real coral skeletons derived using X-ray computed tomography (CT) and constructed using rapid-prototype manufacturing. Two morphologies of S. pistillata from the Red Sea grown in different flow regimes were used. To simplify visualization of the data, velocities were parsed into a series of spherical shells, giving the velocity distributions as functions of distance from coral center for both morphologies. The low-flow morphology distributed flow velocity relatively evenly throughout the interior. In contrast, the high-flow morphology showed a wider range of velocities with regions of flow channeling and flow stagnation. Corals extract nutrients and particles directly from the water that flows past them at rates determined by the chemistry and hydrodynamics of the fluid adjacent to their surfaces. Engineering correlations for bulk mass transfer indicate that nutrient uptake by the coral is limited by diffusion through the boundary layer (Atkinson and Bilger 1992; Bilger and Atkinson 1992; Atkinson et al. 2001). Because uptake of nutrients by surface chemical reactions is fast compared to transport of species from the bulk fluid to the coral surface (Atkinson 1987), this diffusive boundary layer acts as the main barrier to transport into and out of the organism, and thus is the rate-limiting factor. For a given Schmidt number, Sc 5 n/k, where n is the fluid viscosity, k is the diffusivity of the species of interest (e.g., PO 4 ), and the thickness of the boundary layer is a complex function of the fluid velocity adjacent to the surface as well as the local pressure gradient (Kays and Crawford 1993). Indeed, beyond certain simple cases, e.g., flow over a flat surface with a mild pressure gradient, there are no general rules of thumb connecting diffusive boundary layer thickness and, hence, mass transfer rates, to the bulk flow rates that standard field and laboratory methods can measure. Conventional field and laboratory methods (e.g., acoustic and optical Doppler-based flowmeters, or particle image velocimetry) can be used to measure flow around the coral colony exterior, but they cannot be used to map flows within the interior, i.e., between the branches. Given that the bulk of the coral surface area is within this interstitial space of the colony, much of the flow dynamics that is important to mass transfer, and hence to coral physiology and ecology, has generally been inaccessible to measurement. This is important because flow variations within this region may be an important determinant to coral morphology (Kaandorp et al. 2003) and may also determine its susceptibility to bleaching (Nakamura and van Woesik 2001). For example, if the flow is channeled through the coral at relatively high velocities along a few preferred flow * Corresponding author: 1819 paths, then mass transfer will vary dramatically throughout the colony surface (Chamberlain and Graus 1975; Kaandorp et al. 2003). To some extent, these variations might be smoothed out by translocation of nutrients and photosynthates (Rinkevich and Loya 1983) and by oscillatory flows (Reidenbach et al. 2006). In contrast, if the flow is mostly stagnant within the colony, then mass transfer in the interior will be sharply reduced relative to the exterior. Most likely, there are both regions of high velocity and of stagnant flow (Chamberlain and Graus 1975). Thus, detailed flow measurements are needed to assess the degree to which the coral colony interior interacts with the exterior environment and thereby participates in mass exchanges needed by the entire colony. Clearly, computing the flow within the colony by directly solving the Navier Stokes equations is viable given the abilities of current high-performance computing platforms and modern computing techniques for dealing with complex geometries (Mittal and Iaccarino 2005). Yet, even such calculations must be compared with measurements to assess their fidelity, given that turbulence is not deterministic and is still ultimately modeled in the simulations. This was the initial motivation for the present work: to provide data that could be used to validate a computational model of the flow through a single coral (Chang 2007). However, it is clear that because of its novelty, such data would be valuable on its own. Computational results for the coral colonies will be presented elsewhere. Here we present direct measurements of the velocity field throughout the entire volume containing a single coral colony of the scleractinian coral Stylophora pistillata with magnetic resonance velocimetry (MRV). This technique measures three-component velocity data over the domain of interest without requiring optical or acoustic access for each measurement point. As we discuss below, the unprecedented view of the flow inside a coral colony afforded us by MRV reveals the high degree of spatial variability and complexity that exists there as well as highlighting fundamental differences in flow behavior caused by morphological changes induced by flow.

2 1820 Chang et al. Fig. 1. (a) CT scan for S. pistillata with a conventional scanner. This image is a 2D projection of the final compilation of 245 images taken at every 0.7 mm (in the direction out of the page). The image pixel size is 0.35 mm mm. (b) 3D computer-assisted design (CAD) model for low-flow S. pistillata constructed from the CT scan with Mimics TM (Materialise). Methods Overview Scale models of real coral colonies were mounted within a flow channel which was placed within a clinical magnetic resonance imaging (MRI) scanner to measure the full three-dimensional (3D) velocity field around and within the coral colony. While a powerful tool, the use of MRI to measure flows places several significant constraints on any experiment: (1) the flow channel cannot contain any ferrous materials, and it must be small enough to fit within a coil that can provide high resolution data; (2) since the MRI unit s primary function is medical diagnosis, access time is limited; and (3) measuring a single 3D flow field is time consuming in our case approximately 3 h. Taken together, these constraints meant that there were significant limits to the number of cases that could be run. Coral models Rather than use idealizations of coral colonies, real coral geometries were used in the experiments. However, given that the real corals of interest were larger than the channel that would fit within the MRI coil used, digital representations of the corals were obtained so that scale models could be constructed. Two coral morphologies of S. pistillata from high-flow (u mean 5 7cms 21 ) and low-flow (u mean 5 4cms 21 ) environments were chosen for the experiments. These particular coral colonies, which were from the Red Sea near Eilat and which were also used by Reidenbach et al. (2006) in their experiments, have distinctly different morphologies: The low-flow morphology (LFM) has finer branches that tend to extend further out from the center, compared with the high-flow morphology (HFM) which has more compact, thicker branches. The 3D images of these coral skeletons were obtained using X-ray computed tomography (CT). CT can effectively image calcium carbonate, the basis for both bone and coral skeleton (Kaandorp et al. 2003; Chang 2007). For the LFM, a standard CT scanner was used with a resolution of 0.35 mm in-plane and 0.7 mm out-of-plane, resulting in 245 images. Figure 1a shows the two-dimensional (2D) projection of the CT scan for this coral. For the HFM, the Axiom Artis dta angiography suite (Siemens), capable of creating isotropic volume pixels, or voxels, was used. This scan resulted in 290 slices with mm voxel resolution. Using the CT data set, 3D solid models were constructed for both morphologies using the commercial software Mimics TM (Materialise) (Fig. 1b). This computer-aided design (CAD) model was exported to a stereolithography (stl) file for rapid protoype (RP) manufacturing. The coral models were built at the University of Texas El Paso by Dr. Ryan Wicker using acrylonitrile butadiene styrene (ABS) plastic with a fused-deposition modeling (FDM) Maxum System (Stratasys). The LFM and HFM models were scaled by factors of 75% and 90% relative to their parents, respectively. The streamwise (x), cross-stream (y), and vertical (z) extents of the LFM were 9.3 cm, 10.7 cm, and 9.8 cm, respectively. The streamwise (x), cross-stream (y), and vertical (z) extents of the HFM were 12.8 cm, 13.2 cm, and 9.0 cm, respectively. Because of the resolution of the CT scans and the prototype manufacturing, the small roughness scale of the coral surface (e.g., corallite) was smoothed out. While this may affect the finescale fluid dynamics, the turbulence is primarily created by large-scale roughness, as defined by the branches (Hearn et al. 2001). Experiments We used the MRV technique described by Markl et al. (2003), which is based on a 3D, phase-contrast imaging sequence, to measure all three velocity components. This method provided accurate mean-velocity measurements in turbulent flows when results were averaged over repeated scans (Elkins et al. 2004; Elkins and Alley 2007). All experiments were performed using a 1.5-T clinical magnetic resonance (MR) system [GE Signa CV/I (cardiovascular imaging system)], with a single-channel receiver coil designed for human heads. A channel 19 cm wide 3 17 cm tall by 85 cm long was built to fit into this coil (Fig. 2a). A schematic of the flow loop is shown in Fig. 2b. A centrifugal

3 Flow inside a coral colony 1821 pump circulated water at a flow rate of 77 L min 21.A gadolinium-based contrast agent was added to the water to enhance signal intensity and facilitate imaging. A 57-cmlong diffuser section connected the 5.1-cm-diameter inlet to the 17-cm 3 19-cm test-channel cross section. Three screens with differential grid spacing (with lowest void ratio in the center and increasing outward) were installed along the cm length of the diffuser to spread out the flow and to create a more uniform velocity profile at the inlet to the rectangular channel test section. The center of the coral was mounted 35 cm downstream of the inlet. The bulk mean velocity in the test channel was approximately 5 cm s 21, giving a Reynolds number (Re 5 UL/n, where U is the average velocity, L is the lengthscale, and n is the kinematic viscosity) of approximately 5000, based on the height of the coral. While this may be the most appropriate length scale for flow structures resulting from the coral in its entirety, branch diameter may be a more appropriate length scale for the interior flow, because individual branches significantly contribute to flow variations in this region. In this case, we estimated Re for the LFM and Re for the HFM based on diameters for the circular approximation of the branch s cross sections. The experimental velocity of 5cms 21 was chosen for both morphologies in order to isolate the coral geometry as the only variable. The imaging volume consisted of mm-thick slices each with a 28-cm, in-plane field-of-view (FOV) extending from approximately 0.5 colony diameters upstream and 1 diameter downstream from the front and back edges of the coral, respectively. The in-plane resolution in each direction was 1.09 mm, thus defining a 3D voxel approximately 1 mm on each side. Error estimation for MRV depended on the signal-to-noise ratio and the encoding velocity used for the phase contrast measurements (Elkins and Alley 2007). In this experiment, the estimate for the uncertainty in velocity was approximately 0.5 cm s 21. Results Fig. 2. (a) Water channel constructed for the MRV experiment. (b) Schematic of the water flow loop in the MRI scanner. The CT scans allowed us to quantify several simple morphological differences between the two corals (Table 1). Note that more sophisticated descriptions of the morphology are possible (Kaandorp and Kübler 2001), but are likely to be less relevant for describing flow structure differences than they are for documenting morphological complexity and self similarity. We computed the ratio of volume to surface area, an effective branch thickness scale, finding that the HFM branches were approximately 1/3 thicker than those of the LFM. We also computed the ratio of the frontal area, defined by the coral outline, to surface area; as expected, the HFM has significantly more surface area per area facing into the flow. Likewise, a, the ratio of total surface area to planar projected area (Bilger and Atkinson 1992; Falter et al. 2005) was larger for the HFM than for the LFM. Thus in principal, these two measurements suggest that, all else being equal, the HFM should support a higher overall mass flux to the colony. However, as the MRV measurements demonstrated, the HFM in general experienced lower velocities in the interior, which tended to increase the boundary-layer thickness and consequently reduced mass transfer. Finally, the ratio of branch distance to branch radius (which we measured by Table 1. Physical and morphological properties of Low flow (LFM) and High flow (HFM) morphologies of S. pistillata. Low flow High flow u mean (cm s 21 ) 4 7 Ratio of volume to surface area (cm) Ratio of surface area to planar projected area (a) Ratio of frontal area to surface area Ratio of branch distance to branch radius

4 Flow inside a coral colony 1823 enclosed the coral. Average streamwise velocities were calculated in shells of 5-mm thickness at various radial fractions (Fig. 5a). We explored these trends by using different shell sizes and found the same results for shells of different thicknesses; the trends seen in Fig. 5a were therefore not dependent on the choice of shell size. To extend this analysis, the fraction of coral surface area contained in each shell was calculated and plotted with radial distance from the coral center (Fig. 5b). Finally, the normalized mean velocity of the shell was plotted versus the fraction of coral surface area in the shell to show the distribution of mean velocity over the coral surface (Fig. 5c). A small subset of the entire 3D data set is presented in Fig. 6 as sequences of 2D contour plots in planes with different orientations. These contour plots were useful for visualizing the flow around and through each of the coral geometries as well as comparing the flow patterns between the two corals. Figure 6 shows contour plots of the velocity magnitude (m s 21 ) in multiple planes close to the center of the two corals with the coral shown as white. Columns (a) and (b) show planes normal to the y direction for LFM and HFM, respectively. Columns (c) and (d) show planes normal to the z direction for LFM and HFM, respectively. The middle row [row (3)] was the middle of the coral, and each slice was shifted 5 mm from its neighbors. Flow was in the positive x direction. Upon inspecting Fig. 6, one would expect velocities to vary not only with radial distance from the center but also with location relative to the incoming flow. In Fig. 7, velocity data are analyzed spatially by dividing the spherical shells of Fig. 5 into four quadrants relative to the incoming flow: upper front, lower front, upper back, and lower back. The normalized average velocity was plotted as a function of normalized radius, or radial fraction, in these regions for both coral geometries. Discussion The vector field in Fig. 3 shows how the flow is diverted laterally outward, around, and vertically up and over the coral on the upstream side like a baffle, as suggested by earlier flow visualization studies (Chamberlain and Graus 1975; Reidenbach et al. 2006). The flow slowed and recirculated behind the coral colony as a whole as well as behind individual branches. Thus, parcels of water along with what they carry were trapped with longer residence times behind each coral branch than in the passages between them. Moreover, this behavior would imply a much-reduced access to particulate fluxes (e.g., zooplankton) in the lee of each branch than on the forward sides, and for the interior and back of the colony relative to the front, sides, and top of it. This was further exacerbated by the recirculation, which circulated nutrient-depleted water behind each branch. As seen in Fig. 3, flow blockage, channeling, and recirculation are evident throughout the interior, resulting in large spatial variability in the velocity distribution. Where one branch was in front of another, the upstream branch created a wake that significantly reduced the Fig. 5. (a) Normalized average streamwise velocity in the interior as a function of radial distance by fraction of total radius for both low- and high-flow morphologies. (b) Surface area of coral in each shell. (c) Distribution of normalized mean velocities over the fraction of coral surface area as extracted from shell analysis.

5 1824 Chang et al. Fig. 6. Column (a) y-plane slices for low-flow morphology. (b) y-plane slices for high-flow morphology. (c) z-plane slices for lowflow morphology. (d) z-plane slices for high-flow morphology. The middle row [row (3)] is the middle of the coral, and each slice is shifted 5 mm from its neighbors. Flow is in the positive x direction. The colors specify velocity in m s 21. downstream velocity. To the extent that mass transfer was related to local velocity shear, the near-surface velocities shown in Fig. 4 suggest that there should have been much higher local mass transfer in some regions, e.g., forwardfacing branch tips. As expected, the upstream side of the coral was exposed to higher velocity than the downstreamfacing side. However, the figure shows local highs on the tips of many branches, regardless of their orientation or location throughout the coral, which may indicate the relative importance of the tips to mass transfer, i.e., nutrient acquisition or waste metabolite removal, relative to the rest of the coral. The mean streamlines in Fig. 4 serve to illustrate the effects of the coral on the surrounding fluid, showing that flow passing through the periphery and toward the outer edge of the coral retains its high velocity and relatively straight trajectory. In contrast, flow in the center and especially near the bottom of the coral tended to meander and slow down significantly. Thus, the overall distribution of velocities as a function of position in the colony varied significantly. Additionally, the mean streamlines show that the extent of the overall wake behind the coral colony extended more than one colony diameter downstream from the back edge of the coral. Consequently, for densely spaced colonies, the incoming flow would be strongly affected by distance to its upstream neighbor. One effect of the flow diversion by the colony was to reduce the overall supply of material from upstream into the colony. To quantify this reduction, we determined the overall shadow or outline of the coral and then computed the flow through every streamwise slice in the scanned domain. Because the slices at the upstream and downstream edges of the scans tended to have low signalto-noise ratio, those slices were removed from the analysis. The flow that penetrated through the coral interior normalized by the oncoming flow through the coral outline was plotted for both morphologies in Fig. 8. In both cases, the flow that penetrated the interior decreased progressively along the streamwise direction, reaching 35% and 23% of the incoming flow for the LFM and the HFM, respectively. Equivalently, the flow that was diverted by the coral increased progressively in the streamwise direction. The stark difference between the two morphologies is due to the fact that the LFM allowed more flow penetration through its sparser branches. Additionally, because the branches also spread out further (see Table 1), the coral outline defined for the LFM had more voids and thus resulted in a higher fraction of the upstream flow penetrating into the coral interior. In contrast, the HFM was much denser and presented higher resistance to flow, thus resulting in more flow diverted around the colony. Moreover, the flow through the colony decreased more rapidly through the colony for the HFM as compared with the LFM, with approximately 80% of the flow diverted in the former case, as compared to 60% in the latter. A notable difference between the two morphologies was the velocity rebound in the wake, where the LFM velocity increased slightly from 35% to 40%. In

6 Flow inside a coral colony 1825 Fig. 7. Normalized average velocities calculated for spherical shells with 5-mm radial thickness are plotted as a function of normalized radius from the coral centers for four spatial quadrants oriented relative to the streamwise direction: upper front (x solid), lower front (circle solid), upper back (x dashed), and lower back (circle dashed). (a) low-flow morphology and (b) high-flow morphology. contrast, the HFM had a much greater rebound, from 23% to 42%. It is well-known that flows around surface mounted obstacles are accompanied by vortices such as the horseshoe vortex that can wrap around the object, forming streamwise vortices downstream (Mason and Morton 1987). Thus the difference in wake dynamics may be associated with differences in the vortex system around the two corals. Nonetheless, these wake observations imply that the influence of an LFM colony may extend farther downstream than would that of an HFM colony, thus having a greater effect at a fixed distance on mass fluxes for its neighbors downstream. The differences in the average velocity of the spherical shell between the interior (0 70% from coral center) and exterior (70 100% from coral center) for the two morphologies were not dramatic (Fig. 5), with the lowest interior Fig. 8. Fraction of incoming flow penetrating into coral interior and subsequent wake of coral imprint for (a) low-flow morphology and (b) high-flow morphology. The vertical lines denote the front and rear edges of the coral. velocity being 59% of the bulk velocity for the LFM and 48% for the HFM. These differences are comparable to the mass-transfer rate differences between exterior and interior of corals measured by Reidenbach et al. (2006), where gypsum dissolution was used as a proxy for relative velocity measurements. Our data indicate that on average, the LFM with its more intricate and finer branching pattern as compared to the HFM distributed flow speed evenly throughout the interior, where a relatively constant mean velocity existed between 20% and 70% of the radius. In contrast, the HFM, with its thicker branches, tended to channel the flow in the manner described in Chamberlain and Graus (1975), leading to greater variability in the interior flow, as seen in the troughs at 0.3 radial fractions and 0.6 radial fractions in the HFM (Fig. 5). Both corals shared the same distribution of surface area, with the peak surface area occurring at a radius that was 70% of the maximum. Interestingly, this same position separated the nearly constant portion of the velocity curve

7 1826 Chang et al. seen in the interior of the coral from the increasing velocity curve for greater radii. This indicates a clear demarcation between the interior versus exterior hydrodynamic partitions, where the interior is the region where the hydrodynamics is manipulated by the coral, and the exterior is the region where the hydrodynamics is determined by the bulk velocity. While data points were scattered, the highest flow speed was consistently experienced by the outermost shells, as expected. The difference between the interior flow behaviors of the LFM and HFM colonies was qualitatively apparent in the cross-sectional slices shown in Fig. 6 as well. The slices for the LFM (columns a and c) show that there was more open space in the interior between the more sparsely distributed branches of this colony as compared with the HFM (columns b and d). Consequently, the flow tended to be more evenly distributed throughout the interior, as evidenced by the similar velocities. In contrast, the HFM slices show more coral mass. This resulted in significant flow retardation in the lee of many branches. In addition, high-velocity channels are sometimes created by favorable branch alignment when two or more branches lie directly behind one another. One cautionary note is that the observed high-velocity channels may be a function of the way the coral was oriented with respect to the streamwise direction in our experiments which may have been different from the actual orientation of the coral relative to the dominant flow direction where it grew. However, while the location of these channels depends on the orientation in the flow, it seems likely that with a different orientation, similar channels would appear, just in other regions. Therefore, the net effect of channeling should be relatively independent of flow direction. Using the plots in Fig. 6 as a guide, the LFM appears to have distributed the flow relatively uniformly throughout the interior. This allowed the interior of the colony to more actively participate in mass transfer and particle capture. The HFM, in contrast, created larger low-velocity separation zones behind its bigger branches as well as several long, high-velocity channels as an alternative way for the flow to pass through the interior. This may indicate high variation in mass transfer, thus nutrient uptake, as a function of location on the coral surface. It is obvious from the contour plots in Fig. 6 that velocities varied throughout the interior of the coral. The plots in Fig. 8 parse the shell velocity data shown in Fig. 6 into four spatial quadrants relative to the incoming flow: upper front, lower front, upper back, and lower back. The plots show that the front experienced higher velocity than the back. An exception was in the smallest shells in the interior of the coral, where the flow was more tied to the local coral geometry than to the bulk. The velocities of smallest shells in all quadrants were similar despite the significant differences in the velocities of the largest shells. Additionally, the front faces of both morphologies seem to have experienced similar conditions, starting with middle to high velocities (normalized by the bulk mean velocity) in the center which gradually increased as the shells moved outward from the interior (solid lines in Fig. 8). This was not the case for the back faces, where the bottom quadrant consistently experienced lower velocities. This was consistent with the visualizations of the MRV volume (Figs. 5, 7), where wake effects were strongest at the base of the coral with lower velocities and recirculation. Both corals showed strikingly similar trends for all four quadrants. One major difference was that HFM had lower velocity in its top and, especially, bottom back regions, most likely due to its thicker base, trunk, and branches. It is important to remember that the distribution of flow through the coral interior is highly dependent on the upstream flow characteristics. In a canopy environment, where one coral sits in the wake of another coral upstream, the velocity distribution will likely differ from the results shown here. The picture that emerged from these observations is one that suggests extreme variability in mass transfer throughout the colony. Moreover, these variations should be more pronounced from the front to the back of the colony given that mass fluxes also depend on the spatially developing concentration field. If there is high mass transfer at the front of the colony, there will be lower nutrient concentrations at the back, leading to lower mass transfer rates near the back than would be expected based on difference in velocity shear. Thus, one can hypothesize that the low mass transfer portion of the colony must rely on high mass transfer regions to help support the total transfer of materials into and out of the colony, using mechanisms like translocation as described by Rinkevich and Loya (1983). Nonetheless, as shown by Mass and Genin (2008), in unidirectional flows, significant front-to-back asymmetry in distribution of zooxanthellae and eventually in skeleton mass can develop, and therefore there must be limits to the utility of translocation to smooth out spatial variations in mass transfer. On the other hand, in their natural habitat, the corals Mass and Genin studied experienced bi-directional tidal flows and so remained approximately symmetric. Overall, because of the complexity of the coral geometry, it is clear that simple models like periodic arrays of tubes (Eckman 1983), rods (Nepf and Vinoni 2000), or cylinders (Lowe et al. 2005) only bear a very coarse similarity to the flow inside a single coral colony, i.e., all these structural arrangements led to flow channeling and sheltering, as well as to flow diversion around and above the structures. Additionally, the strong effects of the wakes of upstream branches on the flow incident to downstream branches mean that it may be difficult to extrapolate the results of studies with single branches to colony-level fluxes (Sebens et al. 1997) unless the branches are very sparse. More importantly, there is an important difference in scale between our work and that of the studied periodic arrays. Our study focused on flows inside a single structure as opposed to considering a collection of such structures assembled into a canopy (Lowe et al. 2008). When describing flows through and over biological canopies (reefs, polychaete tube arrays, and seagrass beds), the focus is usually on spatially averaged processes such as net momentum or mass transfer, whereas the MRV measurements we present here show details inside one element of what might compose such a canopy. The classical view of a canopy also assumes some spatially statistical homogene-

8 Flow inside a coral colony 1827 ity, whereas here we emphasize the complete absence of any such homogeneity, i.e., that single colonies have notable channels and dead zones with very different shears and speeds, and thus, presumably, very different local rates of mass transfer and particle capture throughout their surfaces. Detailed three-component mean velocity distributions inside two coral-colony interiors were measured using MRV. This noninvasive technique captured not only the effects of the colony as a whole on the flow, but also of the individual branches, which produced wakes that influenced flows around downstream branches. Additionally, two different characteristics for interior flow were identified: the relatively even distribution of flow in the case of the LFM, as opposed to the defined channeling of the HFM. These differences in flow behavior may reflect the way coral colony morphologies adapt to their natural flow environments. These measurements emphasized the high intracolony variability of the potential for mass transfer, behavior that should be accounted for in any model connecting coral morphology and physiology to flow. Acknowledgements The authors would like to express their gratitude to Amatzia Genin of Steinitz Marine Laboratory for generously providing the coral skeletons and indispensable guidance on coral biology, to Ryan Wicker and Frank Medina of the University of Texas at El Paso for providing the models, to Robert Bennett for assistance on the computed tomography, to Michael Markl for initial magnetic resonance scanning, to Lars Saetran of Norwegian University of Science and Technology for help with the magnetic resonance velocimetry experiments, and to Jeff Koseff and Jonah Steinbuck of Stanford University for helpful discussions. We would also like to acknowledge the reviewers for their valuable input. This research was supported by the National Science Foundation grant OCE References ATKINSON, M Rates of phosphate uptake by coral reef communities. Limnol. Oceanogr. 32: , AND R. BILGER Effects of water velocity on phosphate uptake in coral reef-flat communities. Limnol. Oceanogr. 37: , J. FALTER, AND C. HEARN Nutrient dynamics in the Biosphere 2 coral reef mesocosm: water velocity controls NH 4 and PO 4 uptake. Coral Reefs 20: BILGER, R., AND M. ATKINSON Anomalous mass transfer of phosphate on coral reef flats. Limnol. Oceanogr. 37: CHAMBERLAIN, J., AND R. GRAUS Water flow and hydromechanical adaptations of branched reef corals. Bull. Mar. Sci. 25: CHANG, S Small-scale flow variability inside branched coral colonies: Computations and experimental validation. Ph.D. thesis. Stanford Univ. ECKMAN, J. E Hydrodynamic processes affecting benthic recruitment. Limnol. Oceanogr. 28: ELKINS, C. J., AND M. T. ALLEY Magnetic resonance velocimetry: Applications of magnetic resonance imaging in the measurement of fluid motion. Exp. Fluids 43: , M. MARKL, A. IYENGAR, R. WICKER, AND J. K. EATON Full-field velocity and temperature measurements using magnetic resonance imaging in turbulent complex internal flows. Int. J. Heat Fluid Flow 25: FALTER, J. L., M. J. ATKINSON, AND C. F. M. COIMBRA Effects of surface roughness and oscillatory flow on the dissolution of plaster forms: Evidence of nutrient mass transfer to coral reef communities. Limnol. Oceanogr. 50: HEARN, C. J., M. J. ATKINSON, AND J. L. FALTER A physical derivation of nutrient-uptake rates in coral reefs: Effects of roughness and waves. Coral Reefs 20: KAANDORP, J. A., E. A. KOOPMAN, P. M. A. SLOOT, R. P. M. BAK, M. J. A. VERMEIJ, AND L. E. H. LAMPMANN Simulation and analysis of flow patterns around the scleractinian coral Madracis mirabilis (Duchassaing and Michelotti). Phil. Trans. R. Soc. Lond. B. 358: , AND J. E. KÜBLER The algorithmic beauty of seaweeds, sponges, and corals. Springer Verlag. KAYS, W. M., AND M. E. CRAWFORD Convective heat and mass transfer, 3rd ed. McGraw-Hill. LOWE, R. J., J. R. KOSEFF, AND S. G. MONISMITH Oscillatory flow through submerged canopies. Part 1. Velocity structure. J. Geophys. Res. 110: C10016, doi: /2004jc , U. SHAVIT, J. L. FALTER, J. R. KOSEFF, AND S. G. MONISMITH Modeling flow in coral communities with and without waves: A synthesis of porous media and canopy flow approaches. Limnol. Oceanogr. 53: MARKL, M., AND others Time resolved three dimensional phase contrast MRI 4D-flow. J. Magn. Reson. Imaging 17: MASON, P. J., AND B. R. MORTON Trailing vortices in the wakes of surface-mounted obstacles. J. Fluid Mech. 175: MASS, T., AND A. GENIN Environmental versus intrinsic determination of colony symmetry in the coral Pocillopora verrucosa. Mar. Ecol. Prog. Ser. 369: MITTAL, R., AND G. IACCARINO Immersed boundary method. Ann. Rev. Fluid Mech. 37: NAKAMURA, T., AND R. VAN WOESIK Water-flow rates and passive diffusion partially explain differential survival of corals during the 1998 bleaching event. Mar. Ecol. Prog. Ser. 212: NEPF, H. M., AND E. R. VIVONI Flow structure in depthlimited, vegetated flow. J. Geophys. Res. 105: REIDENBACH, M., J. KOSEFF, S. MONISMITH, J. STEINBUCK, AND A. GENIN The effects of waves and morphology on mass transfer within branched reef corals. Limnol. Oceanogr. 51: RINKEVICH, B., AND Y. LOYA Oriented translocation of energy in grafted reef corals. Coral Reefs 1: SEBENS, K. P., J. WITTING, AND B. HELMUTH Effects of water flow and branch spacing on particle capture by the reef coral Madracis mirabilis (Duchassaing and Michelotti). J. Exp. Mar. Bio. Ecol. 211: Associate editor: Christopher M. Finelli Received: 31 July 2008 Accepted: 21 April 2009 Amended: 05 May 2009

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