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Abstract This paper presents a numerical investigation into the aerodynamic characteristics and fluid dynamics of a flying snake-like model employing vertical bending locomotion during aerial undulation in steady gliding. In addition to its typical horizontal undulation, the modeled kinematics incorporates vertical undulations and dorsal-to-ventral bending movements while in motion. Using a computational approach with an incompressible flow solver based on the immersed-boundary method, this study employs topological local mesh refinement mesh blocks to ensure the high resolution of the grid around the moving body. Initially, we applied a vertical wave undulation to a snake model undulating horizontally, investigating the effects of vertical wave amplitudes ( ${\psi }_m$). The vortex dynamics analysis unveiled alterations in leading-edge vortices formation within the midplane due to changes in the effective angle of attack resulting from vertical bending, directly influencing lift generation. Our findings highlighted peak lift production at ${\psi }_m={2.5}^{\circ }$and the highest lift-to-drag ratio (L/D) at ${\psi }_m=5^{\circ }$, with aerodynamic performance declining beyond this threshold. Subsequently, we studied the effects of the dorsal–ventral bending amplitude ( ${\psi }_{\text{DV}}$), showing that the tail-up/down body posture can result in different fore-aft body interactions. Compared to the baseline configuration, the lift generation is observed to increase by 17.3% at ${\psi }_{\text{DV}}$= 5°, while a preferable L/D is found at ${\psi }_{\text{DV}}$= −5°. This study explains the flow dynamics associated with vertical bending and uncovers fundamental mechanisms governing body–body interaction, contributing to the enhancement of lift production and efficiency of aerial undulation in snake-inspired gliding. 

This paper numerically studies the flow dynamics of aerial undulation of a snake-like model, which is adapted from the kinematics of the flying snake (Chrysopelea) undergoing a gliding process. The model applies aerial undulation periodically in a horizontal plane where a range of angle of attack (AOA) is assigned to model the real gliding motion. The flow is simulated using an immersed-boundary-method-based incompressible flow solver. Local mesh refinement mesh blocks are implemented to ensure the grid resolutions around the moving body. Results show that the undulating body produces the maximum lift at 45° of AOA. Vortex dynamics analysis has revealed a series of vortex structures including leading-edge vortices (LEV), trailing-edge vortices, and tip vortices around the body. Changes in other key parameters including the undulation frequency and Reynolds number are also found to affect the aerodynamics of the studied snake-like model, where increasing of undulation frequency enhances vortex steadiness and increasing of Reynolds number enhances lift production due to the strengthened LEVs. This study represents the first study of both the aerodynamics of the whole body of the snake as well as its undulatory motion, providing a new basis for investigating the mechanics of elongated flexible flyers. 

Flying snakes are the only snakes on Earth capable of aerial gliding, taking advantage of fluid dynamic principles to leap from point to point among the trees. During their gliding, the locomotion of aerial undulation is observed. We hypothesize that this locomotion and its associated unsteady vortex dynamics are critical to their aerodynamic performance. However, there is a lack of detailed three-dimensional flow field information around the snake body in gliding due to the difficulties in experimental flow visualizations of live animals. In this study, a computation fluid dynamics (CFD) study has been conducted to study the fluid dynamics of a snake-like gliding. A mathematical equation describing the horizontal undulation motion was applied for constructing snake-like 3D computational models and a series of flow simulations were conducted. An immersed-boundary-method (IBM)-based direct numerical simulation (DNS) flow solver along with adaptive mesh refinement (AMR) was used in the simulation. Specifically, different head positions, corresponding to different horizontal wave shapes and their effect on aerodynamic performance, flow field and wake structures behind the body will be studied. In addition, the dynamic undulating motion is introduced in the model and a CFD simulation is also conducted. Results from this study are expected to bring a step stone to understanding snake-inspired locomotion.