Locomotion trade-offs for rigid bodies: CFD of scaphitid ammonites*

We examine hydrodynamics constraints of swimming strategy among ammonites, extinct squid-like animals from the time of dinosaurs that produced iconic spiral seashells. We consider shape variance among juvenile specimens of Hoploscaphites collected from the Upper Cretaceous Pierre Shale of Montana and synthesize four digital 3D specimens, varying both compression and ornamentation. We use computational fluid dynamic simulations (CFD) in ANSYS Fluent to simulate drag forces within velocities from 1-20 cm/s on specimens 4-5 cm in diameter. Simple ribbing on these shells causes a relative reduction in drag on inflated conch forms. We interpret this as a consequence of premature shear experienced at the ribbing interface along the conch flank, and at the umbilical shoulder. For juvenile scaphites, inflation and ornamentation cause opposing trade-offs in drag force with increasing turbulence. Between two individuals, the inflated form should favor maneuverability and acceleration, while the compressed form should travel greater distance for the same effort. Ribbed ornament appears to help the inflated conch behave more like a compressed conch. Collectively, juvenile scaphites appear to occupy every position within a highly constrained maneuverability-efficiency-speed landscape.