Tuna-Like Swimmers Experience a Fluid-Mediated Stable Side-by-Side Formation

TL;DR

Two self-propelled tuna-like bio-robots spontaneously form a hydrodynamically stable side-by-side arrangement in a constrained cross-stream geometry. The authors combine free-swimming experiments and immersed-boundary CFD to reveal a quasi-steady channeling mechanism: flow acceleration between thick bodies lowers inter-body pressure and generates restorative forces that drive the system toward $\Delta X^*=0$, largely independent of tail phase. Thick bodies ($\tau/L=0.22$) at $\Delta Y^*=0.43$ exhibit a substantial inter-body thrust redistribution with a peak relative thrust of $\Delta C_T$ up to about 0.34, while thin bodies show a much weaker effect. Although the side-by-side state yields modest speed reductions and small increases in cost of transport, the channeling mechanism offers a robust, low-control strategy for maintaining formation cohesion in bio-inspired schools and may inform our understanding of natural tuna schooling.

Abstract

New free-swimming experiments and simulations are conducted on a pair of three-dimensional, bio-robotic swimmers composed of a body and tail section based on Yellowfin tuna, Thunnus albacares. It is discovered that the pair converges spontaneously to a side-by-side schooling formation that is stable to perturbations in the swimming direction at a fixed lateral spacing. We reveal that for close lateral spacings of 43% of the body length and thick, tuna-like bodies with a 22% thickness-to-length ratio, the flow between the swimmers is accelerated in a "channeling effect" due to flow constriction. Consequently, this creates a low-pressure zone that is the primary mechanism generating a fluid-mediated restorative force, thereby making the side-by-side formation hydrodynamically stable. This quasi-steady mechanism makes the stability of the formation insensitive to the phase synchronization between the bio-robots in contrast to previous results for schooling foils. Moreover, in the side-by-side formation tunalike swimmers are seen to have only a small reduction in their swimming speed and a concurrent small rise in their cost of transport. By leveraging this channeling effect, bio-robotic schools may be able to maintain a schooling formation with little or no control. This flow mechanism may also be present in biological schools of tuna-like fish where it may sculpt the formations observed in nature.

Figures (16)

• Figure 1: (a) Definition of coordinate system and non-dimensional distance between swimmers in the streamwise, $\Delta X^*=(x_2-x_1)/L$, and cross-stream, $\Delta Y^*=(y_2 - y_1)/L$, directions. (b) Top view of tuna-like and thin-tuna geometries and their respective maximum thickness to body length ratio $\tau/L$.
• Figure 2: (a) Isometric view of the experimental setup. (b) Schematics of the air-bearing rail and robotic platform. (c) Schematics of the wireless actuation and embedded data acquisition. Laser distance sensors measure the position of each swimmer in time. Infrared (IR) pulses control the kinematics remotely. Unconstrained platforms 1 and 2 are identical. Grey arrows represent flow of actuation signals, and the blue arrows represent flow of data measurement signals. The torque data is stored locally by an SD card and retrieved over WiFi at the end of the experiment. The position of the bio-robots and measured torque signals can be synchronized in post-processing using the IR pulses as a reference clock. (d) Detailed view of the bio-robot tail, peduncle and caudal fin. (e) Air-bearing spurious force (blue line) calculated from the trajectory of the carriage (black line) at zero flow. (f) Drag force $\overline{F}_{\text{drag}}$ calculated from the trajectory of the carriage (dashed black line) for the bio-robot at rest subject to the freestream $U$.
• Figure 3: Hydrodynamic performance of the tuna-like bio-robots swimming in isolation. Blue: Tuna1; Orange: Tuna2. All data is averaged over three trials. Shaded area indicates the standard deviation of the vertical axis; horizontal bars represent the standard deviation of the horizontal axis. (a) Time-averaged swimming speed (cruising speed) in body lengths per second as a function of the dimensionless tail beat amplitude. (b) Strouhal number as a function of swimming speed. (c) Power coefficient as a function of swimming speed. (d) Cost of transport as a function of swimming speed.
• Figure 4: (a): Illustration of the surface meshes and virtual skeleton used to assign the kinematics to the computational model. The "head-tail" and "pivot" joints align with the locations at which the tail and caudal fin surfaces rotate on the tunabot model in Figure \ref{['fig:exp_setup']}(d). (b) Close-up view of the prescribed kinematics during the right (R) flap and left (L) flap that align with the experiments. The "head-tail" joint angle was prescribed as an 18$^{\circ}$ amplitude (peak-to-peak) sinusoidal function. The "pivot" joint angle was assigned a 30$^{\circ}$ amplitude (peak-to-peak) sinusoidal function that lagged the "head-tail' joint by 90$^{\circ}$ thereby producing the tuna-like flapping motion.
• Figure 5: Schematic of the computational domain. (a) Illustration of grids (every 4th is shown to improve visibility) and velocity boundary conditions on the domain boundaries. (b) Close-up view of the mesh refinement regions surrounding each body, along with the definition of the spatial arrangement in the simulations.