In-line swimming dynamics revealed by fish interacting with a robotic mechanism

Abstract

Schooling in fish is linked to a number of factors such as increased foraging success, predator avoidance, and social interactions. In addition, a prevailing hypothesis is that swimming in groups provides energetic benefits through hydrodynamic interactions. Thrust wakes are frequently occurring flow structures in fish schools as they are shed behind swimming fish. Despite increased flow speeds in these wakes, recent modeling work has suggested that swimming directly in-line behind an individual may lead to increased efficiency. However, only limited data are available on live fish interacting with thrust wakes. Here we designed a controlled experiment in which brook trout, Salvelinus fontinalis, interact with thrust wakes generated by a robotic mechanism that produces a fish-like wake. We show that trout swim in thrust wakes, reduce their tail-beat frequencies, and synchronize with the robotic flapping mechanism. Our flow and pressure field analysis revealed that the trout are interacting with oncoming vortices and that they exhibit reduced pressure drag at the head compared to swimming in isolation. Together, these experiments suggest that trout swim energetically more efficiently in thrust wakes and support the hypothesis that swimming in the wake of one another is an advantageous strategy to save energy in a school.

Keywords: fish schooling; fluid dynamics; in-line swimming; physics of living systems; robotics; thrust wakes.

Figure 1.. Schooling positions with hydrodynamic benefits.

(A) Swimming side-by-side can increase thrust and efficiency by making use of the channeling effect (Ashraf et al., 2017; Daghooghi and Borazjani, 2015). (B) Leading swimmers benefit from higher thrust production due to increased effective added mass at their trailing edge stemming from the blockage of the water in close proximity to trailing swimmers (Bao and Tao, 2014; Saadat et al., 2021). (C) Trailing fish face reduced oncoming flows between two leading fish when swimming in a diamond formation (4). (D) Leading-edge suction provides propulsive thrust for a fish in a trailing position (Kurt and Moored, 2018; Maertens et al., 2017; Saadat et al., 2021).

Figure 2.. Experimental setup.

Flapping foil with 2 degrees of freedom (yaw and sway) generating a fish-like thrust wake in the flow tank. Trout swam in the dark while we captured the kinematics by means of high-speed cameras from a bottom and side view and using infrared lights for illumination. Low light in the tank upstream of the flapping foil allowed fish to orient. In separate experiments, we captured the flow dynamics using particle image velocimetry. We were able to record the entire flow field around the fish by using two lasers (in front and behind) simultaneously.

Figure 2—figure supplement 1.. Comparison of flapping foil wake and fish wake.

(A) Velocity field of the wake behind the flapping foil: red and blue regions indicate counterclockwise and clockwise vorticity, respectively. The average speed profile of the region within the dashed rectangular region is shown on the right. (B) Corresponding plots of the wake behind a steadily swimming trout. Note that even though the flapping foil is rigid and the fish tail is flexible, it is possible to parametrize the motion of the robotic flapper to achieve similar tail tip excursions.

Figure 3.. Body kinematics in thrust wakes.

(A) Reduced tail-beat frequencies and (B) reduced overall phase lags for small (n = 4) and large (n = 6) trout swimming in the thrust wake compared to steady swimming at the same flow tank speed. (C) Illustration of the bending pattern by means of joint angles (rainbow colored lines) along the body. Black markers indicate the bending phase.

Figure 3—figure supplement 1.. Head and tail amplitudes.

Body amplitudes represented as percentage of the body length (BL) for small (n = 4) (A, B) and large (n = 6) (C, D) trout. Head (A, C) and tail (B, D) amplitudes show a slight trend toward increased tail amplitude in the thrust wake but are not significantly different compared to steady swimming.

Figure 4.. Phase difference between foil and fish.

(A) Linear relationship (n = 10) between phase difference and distance from the foil for fish swimming in-line in the thrust wake. Video 3 shows videos of the individual data points 1–10. (B) Distance is measured between the trailing edge of the foil (R1) and the leading edge of the fish (R2). The phase difference is measured between trailing edges of the foil (R1) and the fish (R3).

Figure 5.. Interactions between fish and vortices.

Two representative sequences over one swimming cycle with ventral view of trout station-holding in the thrust wake near the foil at distance d1 with double-sided vortex interactions (A–F) and located more downstream at d2 with single-sided vortex interactions (G–L). Oncoming vortices from the flapping foil are intercepted by trout in the wake. The vortices stay attached on one side depending on their orientation and ‘roll’ downstream along the body (velocity fields shown after subtraction of mean flow speed).

Figure 6.. Reduced head pressure in the thrust wake.

Average pressure fields of a trout swimming in free-stream flow (A) and in the thrust wake of a flapping foil (B) show reduced positive pressures (46% decrease) around the head despite increased oncoming flow. Consistent instantaneous positive pressures over time are present under free-stream flow conditions (C1–C4). Corresponding instantaneous pressure fields display alternating positive and negative pressures around the head in the thrust wake over time (D1–D4).

Figure 6—figure supplement 1.. Reduced average head pressures in thrust wakes.

(A) Trout swimming in the thrust wake exploiting single-sided vortex interactions and 45% decrease in head pressure compared to free-stream swimming. (B) Second example of trout exploiting double-sided vortex interactions with 86% decrease in head pressure found.