Computational fluid dynamics modeling of fossil ammonoid shells

Abstract

We use three-dimensional (3D) numerical models to examine critical hydrodynamic characteristics of a range of shell shapes found in extinct ammonoid cephalopods. Ammonoids are incredibly abundant in the fossil record and were likely a major component of ancient marine ecosystems. Despite their fossil abundance we lack significant soft body remains, which has made it historically difficult to investigate the potential life modes and ecological roles that these organisms played. By employing numerical tools to study how the morphology of a shell affected an ammonite's hydrodynamics, we can build a foundation for hypothesizing and testing changes in the organism's capabilities through time. To achieve this goal, the study was carried out in two major steps. First, we applied a number of simulation methods to a known problem, the drag coefficient of a half-sphere, to select the most appropriate modeling method that is accurate and efficient. These were further checked against previous experimental results on ammonoid hydrodynamics. Next, we produced 3D models of the ammonoid shells using Blender and Zbrush where each shell model emulated a specific fossil ammonoid, recent Nautilus, or an idealized shell forms created by systematically varying shell inflation and umbilical exposure. We test the hypothesis that both the overall shell inflation and umbilical exposure will increase the drag experienced by a similarly sized ammonoid shell as it moves through water relative to other morphologies. ANSYS FLUENT was employed to execute the study. We further compare our simulation results to published experimental measurements of drag on ammonoid fossil replicas and live Nautilus. The simulation results provide accuracy within an order of magnitude of published values, across the tested range of water flow velocities (1-50 cm/s). The simulated drag measurements demonstrate a first-order sensitivity to shell inflation, with a second-order effect from umbilical exposure. The impact of a larger umbilical exposure (shells that are more evolute) is minimal at low velocities, but substantial at higher velocities. We conclude that the overall shell inflation and umbilical exposure influence an individual shell's drag coefficient, therefore, influence the hydrodynamic efficiency.

Recent advances in heteromorph ammonoid palaeobiology

“…(2) Virtual models Virtual models include mathematical models and simulated conchs, either generated ex nihilo or from tomographic data (Hoffmann et al, 2014;Naglik et al, 2015;Lemanis, Zachow & Hoffmann, 2016;Naglik, Rikhtegar & Klug, 2016;Hebdon, Ritterbush & Choi, 2020). Trueman (1941) first attempted to calculate the buoyancy and hydrostatic orientation of several heteromorph conchs, taking the body chamber length versus total conch length into account.…”

Computational Fluid Dynamics and its Applications in Echinoderm Palaeobiology

“…This hypothesis testing framework can be extended further through comparative analyses of multiple taxa, both within and among groups, thereby enabling the assessment of evolutionary patterns (e.g. Wroe et al, 2018;Gutarra et al, 2019;Troelsen et al, 2019;Hebdon et al, 2020;Rahman et al, in press).…”

“…Furthermore, models of hypothetical morphologies could be created to investigate the function of specific characters (e.g. Shiino & Kuwazuru, 2010;Shiino et al, 2012;Rahman et al, 2015a;Darroch et al, 2017;Gutarra et al, 2019;Hebdon et al, 2020). Thus, previously untestable hypotheses are now open to interrogation using CFD, facilitating more rigorous studies of the relationship between form, function and evolution in fossil echinoderms.…”

“…Shiino and colleagues subsequently applied the technique to brachiopods (Shiino et al, 2009;Shiino & Kuwazuru, 2010, 2011 and trilobites (Shiino et al, 2012(Shiino et al, , 2014. More recently, CFD has been used to study extinct vertebrates (Bourke et al, 2014(Bourke et al, , 2018Kogan et al, 2015;Liu et al, 2015;Wroe et al, 2018;Dec, 2019;Gutarra et al, 2019;Troelsen et al, 2019), Ediacaran organisms (Rahman et al, 2015a;Darroch et al, 2017;Gibson et al, 2019), ammonoids (Hebdon et al, 2020) and fossil echinoderms (Rahman et al, 2015b, in press;Dynowski et al, 2016;Waters et al, 2017).…”

Ancient life and moving fluids

“…Fluid dynamics experiments have provided rich insights into the character of fluid–organism interactions in the palaeontological record; the applications of these techniques are continuing to grow, and this necessitates in‐depth examples that include specifics of experimental design and interpretation. Whereas Rahman (2017) and Hebdon, Ritterbush, & Choi (2020) present pragmatic approaches to conducting CFD experiments (and review a breadth of palaeontological CFD studies), here we present a more theory‐based approach to CFD focused on the underlying physics. Moreover, we provide an alternative, more robust application of CFD for future palaeontology studies.…”