DOI: 10.5061/dryad.fxpnvx103
title: Supplementary data for: Hydrodynamic insights into the palaeobiology of the Ediacaran rangeomorph Fractofusus misrai

description: The Ediacaran of Newfoundland preserves some of the oldest complex
 macroscopic communities several of which are dominated by the
 fractal-like rangeomorph genus Fractofusus. Here we use computational
 fluid dynamics and a detailed reconstruction of Fractofusus misrai to
 document for the first time hydrodynamic phenomena associated with this
 sediment-reclining organism and its rangeomorph elements that: are
 relevant to interpreting feeding strategies, explain the recently
 documented rheotropic growth oblique to currents, and provide insights
 into their impact on the Ediacaran seafloor. Obliquely oriented
 Fractofusus are common, likely representing a compromise between maximized
 aspect ratio and minimization of drag. Flow patterns on the upper surface
 of Fractofusus are consistent with the collection of dissolved and finely
 particulate nutrients, as well as gas exchange. Fractofusus produce a long
 wake downstream, demonstrating that reclining Rangeomorpha had potential
 to modify sedimentation patterns on the ancient seafloor by potentially
 allowing deposition of fine grained bypassing sediment.
description: Geometry of <em>Fractofusus
 misrai</em> The three-dimensional models of
 <em>F. misrai </em>were created using ZBrush Pixologic, Inc.
 (https://www.maxon.net/en/zbrush; by R. Nicholls), then post-processed
 using Rhinoceros 3D v.7 (https://www.rhino3d.com) and Blender v.3.4.1
 (https://www.blender.org). The geometry was built as a smoothed three
 million polygon mesh, capturing three orders of rangeomorph branching.
 Scaling followed published fossil dimensions, and geometries were oriented
 according to the statistical clusters in Pérez-Pinedo et al. 2023.
 Finally, results were analyzed with the post-processing visualization
 engine Paraview (https://www.paraview.org). Computational Fluid dynamics
 (CFD) Discretization and
 sensitivity tests were conducted to determine optimal mesh sizes,
 balancing anatomical resolution with computational efficiency (computing
 cores, CPU usage; Figs. S1-S2) at which results are independent of the
 mesh size. <em>Fractofusus misrai</em> geometries, consisting
 of approximately 300,000 to 500,000 polygons, and the corresponding FVRs
 were meshed using Simscale standard-finite-volume meshing algorithms with
 automatic sizing and a medium factor fineness. The resulting mesh consists
 of tetrahedral and hexahedral elements. Various mesh fineness factors and
 region refinements were applied around the fossil geometry to explore the
 ideal computational parameters. Simulations of incompressible water flow
 [density (ρ) ≃ 1,000 kg/m3; dynamic viscosity (μ) ≃ 0.001 kg/(m⋅s)] around
 the reconstructed <em>F. misrai </em>geometry were performed
 using CFD Simscale software (https://www.simscale.com). Reynold numbers
 (Re) were calculated based on the characteristic length of Fractofusus (L
 <sub>0.05, 0.15, 030</sub>) ranging from 2683 ~ 64411 (Table.
 S1). Our flow regimes are around the turbulent transition for flows around
 an obstacle Re 20000. However, it is important to note that our
 reconstructed fossil geometry shows a very complex rough surface which
 results in ‘tripped’ boundary layers leading to critical implications in
 Reynolds number thresholds, meaning it is possible to have turbulent flows
 at lower Reynolds numbers. Nevertheless, the aim of this study is to
 simulate the turbulent hydrodynamic conditions experienced by
 <em>Fractofusus</em> on the seafloor during the interval prior
 to the sediment-laden obrution events that smothered and killed them. The
 clear-water inter-turbiditic background currents travelled at low
 velocities over vast distances interacting with the roughness of the
 seafloor. In doing so they could be expected to have encountered
 innumerable obstacles of variable shapes and sizes, including seafloor
 topography (pits, mounds, ripples, scours, clasts, the bodies of living
 and dead erect and reclining organisms, channelization, etc). That is to
 say that the fronds we see on the Ediacaran bedding planes were not the
 first obstacles that the passing current was exposed to. Even if a such a
 current passed over a smooth seabed for such long distances, the skin
 friction alone would ensure turbulence at the velocities typical of modern
 deep ocean settings. Direct measurements of flow at the seafloor
 demonstrates persistent (turbulent) currents even from the deep
 featureless ocean abyssal plain. Additionally, oceanographic measurements
 estimate the viscous sublayer beneath abyssal currents, based on seafloor
 current data, to be ~5 mm. Fractofusus and most other sources of seafloor
 roughness would have projected through the viscous sublayer serving to
 maintain turbulent conditions at the Ediacaran seafloor. Reynolds numbers
 associated with modern boundary layers are of order
 10<sup>6</sup> to 10<sup>7</sup>. In order to
 simulate currents of comparable strength (U ~ 10 cm/s; U/u* ~ 30–35)
 K-Omega Shear Stress Transport SST model was used to solve the
 Reynolds-averaged Navier–Stokes (RANS) equations, with a stationary solver
 used to compute the steady-state solution across all simulations. This
 model is known to better predict flow separation patterns than most RANS
 models. Additionally,  laminar model simulations covering the entire
 spectrum of modelled sizes, velocities, and orientations were tested for
 comparison, though laminar flows are not expected in natural deep marine
 settings (Table. S1). The computational domain consisted of a
 three-dimensional rectangular FVR, measuring 400cm x 200cm x 40cm allowing
 fully developed flows. A velocity inlet condition was fixed at the -X end
 of the FVG with three different flow velocities (U<sub>x</sub>
 = 0.05 m/s, 0.1 m/s, 0.2 m/s) while a zero-pressure outlet boundary
 condition was applied on the opposite +X end. The boundaries on the sides
 and top featured wall slip-boundary conditions, whereas the lower boundary
 and the F. misrai geometry were assigned no-slip boundary conditions.
 Lastly, our palaeobiological reconstruction of <em>F.
 misrai</em> was affixed to the computational domain on the bottom
 boundary. The organism reconstructions were modelled in three different
 sizes: small (5cm x 1.5cm), medium (16cm x 5cm), and large (30cm x 10cm)
 (Figs. 4, S3-S5). These were positioned in different orientations with
 respect to the flow: parallel (0º), and perpendicular (90º) as well as
 oblique (35º-52º) based on the clusters determined by Pérez-Pinedo et al.
 2023. Flow dynamics from the somewhat analogous modern cold-water
 coral-rich areas in southwest Grand Banks were used to characterize the
 background clear water, turbulent, flow regimes from the Capelin Gulch
 site.The results were compared to a null model in the form of an ellipse
 lacking rangeomorph elements and fully merged into the bottom boundary
 without projecting primary branches. The Velocity magnitude
 (U<sub>x</sub>) and streamlines were visualized and drag
 forces (FD) were computed for each simulation by integrating pressure and
 skin-friction over the boundary. The distribution of the pressures and
 viscous (shear) forces along the elements were integrated, all the overall
 forces and moments calculated. To compute FD, the projected (frontal) area
 of the fossil geometries was calculated (Table. S1). Due to meshing
 difficulties, FD values were calculated using a small millimetre-scale
 base for F. misrai that was bound to the bottom boundary. Finally, FD was
 explored by decomposing the normal force of pressure for each element of
 the surface mesh. 
description: # Supplementary data for: Hydrodynamic insights into the palaeobiology of
 the Ediacaran rangeomorph Fractofusus misrai
 [https://doi.org/10.5061/dryad.fxpnvx103](https://doi.org/10.5061/dryad.fxpnvx103) Supplementary materials include: 1) computational fluid dynamics (CFD) results from discretization and sensitivity tests conducted to determine optimal mesh sizes, balancing anatomical resolution with computational efficiency (Figs. S1-S3); 2) CFD simulation results from different sizes of *F.misrai* and general view of streamlines (Figs. S4-S6); 3) CFD simulation results from null models (Fig. S7); 4) flow velocity profile (Fig. S8); 5) all numeric results from CFD simulations (Table S1); 6) the *Fractofusus misrai* geometry; and 7) CFD simulation results.  ## Description of the data and file structure Fig. S1-S3 show different mesh sizes for both the flow volume region (FVR) and the *F. misrai* geometry. *Fractofusus misrai* geometries, consisting of approximately 300,000 to 500,000 polygons, and the corresponding FVRs were meshed using standard algorithms with automatic sizing and a medium factor fineness. The resulting meshes consisted of approximately 2-4 million cells and 500.000-1 million nodes (Fig. S2). Figs. S4-S5 show the CFD results from different sizes of *F. misrai*. Both small (Fig. S4) and medium (Fig. S5) *F. misrai* are displayed in different orientations relative to the simulated flow from (left to right). Both orientations show the eddying at the frond margin. Current perpendicular *F. misrai* also shows weak vortices on the upper surface of the frond both upcurrent of the axis of the frond, and also in the lee of the axis. Figure S6 shows a general view of streamlines coloured according to velocity (U<sub>x</sub>) around different orientations of *Fractofusus misrai*. Fig. S7 shows CFD simulations of null models. Figure S8. shows th velocity profile (Ux) along vertical axis (z) from the bottom boundary of the fluid domain around Fractofusus misrai. Table S1. Shows CFD simulations numeric results. Reference area is the exposed (frontal) area to the flow and reference length in the length along the x axes. The *F. misrai* geometry is available. The intermediate size (15 cm) *F. misrai* CFD simulation set is available. Remaining results can be normalized using scaling laws. Additional results are available upon request.  ## Code/Software The three-dimensional models of *F. misrai* were created using ZBrush Pixologic, Inc. ([https://www.maxon.net/en/zbrush](https://www.maxon.net/en/zbrush); by R. Nicholls), then post-processed using Rhinoceros 3D v.7 ([https://www.rhino3d.com](https://www.rhino3d.com)) and Blender v.3.4.1 ([https://www.blender.org](https://www.blender.org)). Finally, results were analyzed with the post-processing visualization engine Paraview ([https://www.paraview.org](https://www.paraview.org)). Simulations of incompressible water flow were performed using CFD Simscale software ([https://www.simscale.com](https://www.simscale.com)).