Vortex Dynamics from Burst-and-Coast Motion of Anguilliform and Carangiform Swimmers

TL;DR

The paper investigates how burst-and-coast versus continuous undulation in anguilliform and carangiform swimmers shapes three-dimensional wake dynamics and hydrodynamic forces. Using a high-fidelity $Re=3000$ immersed-boundary CFD approach with traveling-wave kinematics and varying duty cycle $DC$ and Strouhal number $St$, it quantifies near-body vortices, wake bow angles, vortex circulation, and pressure-driven loads. The study finds bow-shaped wakes at low-to-moderate $DC$, inward-shifting vortex rows as $DC$ increases, and higher $St$ increasing drag in intermittent swimming, with distinct differences between eel-like and jackfish kinematics. These insights connect physiology and kinematics to vortex dynamics, informing energy-efficient control strategies for bio-inspired underwater robots.

Abstract

Fish perform various propulsive maneuvers while swimming by generating traveling waves along their bodies and producing thrust through tail strokes. Anguilliform swimmers spread motion along the body, while carangiform swimmers' motion is more prominent near their tails. Many species also switch between continuous undulation and intermittent swimming, such as burst-and-coast maneuver, which can save energy but can also change the wake structure and hydrodynamic forces. Our current study aims at explaining} how duty cycle (DC), undulatory gaits, and Strouhal number (St), shape the near-body vortices, overall wakes, and the hydrodynamic forces. We carry out three-dimensional simulations at Re = 3000 for flows around an eel (anguilliform) and a Jack Fish (carangiform) for DC = 0.2-1.0 and St = 0.30 and 0.40. Our results reveal that the burst-and-coast motion for both swimmer produce bow-shaped wakes, the two rows of which on the sides approach each other to form a more coherent wake as DC is increased to 1.0 that corresponds to the wake of continuously undulating swimmers. It is also found that the intermittent motion at a higher Strouhal number produces more drag, contrary to the continuous undulatory kinematics. We further investigate this behavior by quantifying the strengths of vortices produced around the two swimmers and their instantaneous kinematic metrics. A detailed analysis for the role of different body sections in the production of unsteady streamwise forces is also presented. These insights provide important connections between the swimmers' physiologies, their kinematics, and the governing vortex dynamics to attain certain hydrodynamic metrics for designing next-generation autonomous bio-inspired underwater robots.

Figures (14)

• Figure 1: (a) Flow domain with specifc boundary conditions on its sides and the mesh regions around a swimmer's body, (b) physiology of a Jack Fish, and (c) geometrical features of an eel
• Figure 2: Undulatory kinematic profiles for the (a) anguilliform and (b) carangiform modes, and (c) the kinematic profiles of the swimmer's tail during burst-and-coast motion with different duty cycles
• Figure 3: Vortex structures around the anguilliform swimmer at the end of the undulation cycle in 5 modes for ($a_1$ to $e_1$) $\hbox{St} = 0.3$ and ($a_2$ to $e_2$) $\hbox{St} = 0.4$.
• Figure 4: Vortex structures around the carangiform swimmer at the end of the undulation cycle in 5 modes for ($a_1$ to $e_1$) $\hbox{St} = 0.3$ and ($a_2$ to $e_2$) $\hbox{St} = 0.4$.
• Figure 5: Vorticity $(\omega_z)$ at $z = 0$plane for $\hbox{DC} = 0.4$ at $\hbox{St} = 0.3$ (a) anguilliform swimmer, (b) carangiform swimmer.