Dynamical Characteristics of the Body-Caudal Fin Joint of a Carangiform Swimmer and its Influence on Hydrodynamics

TL;DR

A computational framework of a Jackfish-inspired swimmer with an independently mounted caudal fin that pitches passively under fluid forces and a nonlinear torsional spring reveals that nonlinear peduncle mechanics naturally regulate amplitude, phase, and recoil.

Abstract

The hydrodynamics of fish swimming depend on the interaction between the undulation of the body and the flapping of the caudal fin. This study develops a computational framework of a Jackfish-inspired swimmer with an independently mounted caudal fin that pitches passively under fluid forces and a nonlinear torsional spring. The fin synchronizes with the body when damping and stiffness parameters are tuned correctly, producing passive pitching that closely resembles to the displacement of the actively pitching tail. At Re = 3000, synchronized passive pitching generates coherent hairpin and ring vortices that reinforce streamwise momentum and contribute to thrust, whereas larger phase differences lead to wake spread in lateral direction and drag-dominated behavior. These results reveal that nonlinear peduncle mechanics naturally regulate amplitude, phase, and recoil, offering a biologically inspired pathway toward underwater robotic design using passive kinematics.

Figures (19)

• Figure 1: Physiological details of the Jack fish-like swimmer at (a) a static position (${t}/{\tau} =0$), (b) mid-oscillation instant (${t}/{\tau} =0.55$) and characterization of the body-tail joint, and (c) its side view with dimensional features
• Figure 2: Computational domain and boundary conditions. (a) Three-dimensional domain with XY-, XZ-, and YZ-planes, (a1) fish geometry (trunk and caudal fin), and (a2)-(a3) surface mesh. (b) XZ-plane showing domain extent ($16L$) and downstream wake refinement ($RF$) ($4.5L$). (c) YZ-plane showing cross-sectional domain ($10L \times 8L$) and local mesh refinement around the swimmer.
• Figure 3: Grid-independence study. Instantaneous vorticity fields for (a) coarse ($14$M), (b) medium ($29$M), and (c) fine ($56$M) grids. Time histories of (d) drag coefficient $C_D$ and (e) lift coefficient $C_L$ of the swimmer over one oscillation cycle, respectively.
• Figure 4: Validation of the thrust coefficient $C_T$ obtained using the present methodology against Khalid et al. khalid2021larger for different wavelengths, (a) $\lambda = 0.925L$, (b) $\lambda = 1.05L$, and (c) $\lambda = 1.25L$ over one oscillation cycle.
• Figure 5: Synchronization map of passively pitching tail, (a) variation of the synchronization parameter $\zeta$ with tuning parameter $n$, showing asynchronous and synchronous pitching regimes (Modes 1--7). Dashed lines indicate constant phase-locking trends. (b) Corresponding pitching frequency $f_p$ as a function of $\zeta$, with the dashed line denoting the active heaving frequency.