Mechanics of Undulatory Swimming in a Frictional Fluid

Abstract

The sandfish lizard ( Scincus scincus) swims within granular media (sand) using axial body undulations to propel itself without the use of limbs. In previous work we predicted average swimming speed by developing a numerical simulation that incorporated experimentally measured biological kinematics into a multibody sandfish model. The model was coupled to an experimentally validated soft sphere discrete element method simulation of the granular medium. In this paper, we use the simulation to study the detailed mechanics of undulatory swimming in a “granular frictional fluid” and compare the predictions to our previously developed resistive force theory (RFT) which models sand-swimming using empirically determined granular drag laws. The simulation reveals that the forward speed of the center of mass (CoM) oscillates about its average speed in antiphase with head drag. The coupling between overall body motion and body deformation results in a non-trivial pattern in the magnitude of lateral displacement of the segments along the body. The actuator torque and segment power are maximal near the center of the body and decrease to zero toward the head and the tail. Approximately 30% of the net swimming power is dissipated in head drag. The power consumption is proportional to the frequency in the biologically relevant range, which confirms that frictional forces dominate during sand-swimming by the sandfish. Comparison of the segmental forces measured in simulation with the force on a laterally oscillating rod reveals that a granular hysteresis effect causes the overestimation of the body thrust forces in the RFT. Our models provide detailed testable predictions for biological locomotion in a granular environment.

Author Summary

The sandfish lizard uses body undulation to propel itself within granular media (sand). Previously we developed a numerical simulation model consisting of an experimentally validated multi-particle model of the granular medium, and a sandfish model with prescribed body deformation (a traveling sinusoidal wave with parameters measured from biological experiment). We used the simulation to capture average swimming speed and compared predictions to our previously developed resistive force theory (RFT) for granular media. In this paper, we use the numerical model to perform more detailed analysis of the mechanics of sand-swimming in a so-called “granular frictional fluid”. These include center-of-mass kinematics, force distributions along the body, effects of body and head shape, power generation and dissipation. We discuss how these aspects of sand-swimming compare to those for swimmers (like nematodes and eels) in true fluids. We use the numerical model to reveal how transients during start-up in granular drag generates discrepancies between the simulation and the RFT predictions. The predictions from our models can give insight into locomotor capabilities, musculoskeletal structure and morphological features of sand-swimming animals. These results may also provide guidance for the design and control of sand-swimming robots.