# On the Fluid Dynamical Effects of Synchronization in Side-by-Side Swimmers

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

#### Particle Image Velocimetry

## 3. Results

#### 3.1. Cruising Speed

#### 3.2. Flow Field Measurements

## 4. Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

PIV | particle image velocimetry |

NND | nearest-neighbor distance |

2D | two-dimensional |

3D | three-dimensional |

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**Figure 1.**Schematic diagrams of the experiment with two self-propelled swimmers in a side-by-side configuration. Each foil is held by an independent air-bearing rail (

**left**) and actuated by an oscillating pitching motion of an axis that holds the foil from one extremity (

**right**).

**Figure 2.**Two image sequences are presented with the two foils actuated in-phase (

**top**) and in anti-phase (

**bottom**). The camera is placed at a fixed position below the water tank, and the swimming direction is directed toward the top of the figure. Time in these frame sequences goes from left to right, with an interval between frames of 0.24 s. The initial acceleration phase is not shown. The time stamp on each frame is counted with respect to $t=0$ when the oscillations start from rest. The case shown here corresponds to $d/L=0.6$ and $f=3$ Hz. The size of the visualization window is approximately $L\times 2L$ (0.15 × 0.3 m).

**Figure 3.**(

**left**) Tracking of a typical swimming trajectory. Three different runs are shown with the fit used to compute the final velocity, i.e., the slope of the trajectory at the end of the run. (

**right**) Final average cruising velocity of the two foils normalized by the velocity of a foil swimming alone plotted as a function of the separation between the foils and of the synchronization phase.

**Figure 4.**(

**Top**row) Snapshot of a typical instantaneous velocity field for a single swimmer (left) and a pair of swimmers in phase ($\varphi =0$) and anti-phase ($\varphi =\pi $) (middle and right frames, respectively). (

**Bottom**row) Corresponding vorticity fields. The field of view of the PIV windows is 265 × 154 mm.

**Figure 5.**Sequence of vorticity fields over one period of undulation for in-phase ($\varphi =0$,

**left**column) and anti-phase ($\varphi =\pi $,

**right**column) synchronizations. The field of view of the PIV windows is 265 × 154 mm.

**Figure 6.**Velocity profiles ${u}_{x}\left(y\right)$ in the wake of the swimmers over one period (dashed lines) and their average ${\overline{u}}_{x}\left(y\right)$ (solid line) for in-phase ($\varphi =0$, left) and anti-phase ($\varphi =\pi $, right) synchronizations.

**Figure 7.**Time average (

**top**) and rms (

**bottom**) of the kinetic energy field ${E}_{kin}=\frac{1}{2}({u}_{x}^{2}+{u}_{y}^{2})$ over the full run for in-phase ($\varphi =0$,

**left**) and anti-phase ($\varphi =\pi $,

**right**) synchronizations.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Godoy-Diana, R.; Vacher, J.; Raspa, V.; Thiria, B.
On the Fluid Dynamical Effects of Synchronization in Side-by-Side Swimmers. *Biomimetics* **2019**, *4*, 77.
https://doi.org/10.3390/biomimetics4040077

**AMA Style**

Godoy-Diana R, Vacher J, Raspa V, Thiria B.
On the Fluid Dynamical Effects of Synchronization in Side-by-Side Swimmers. *Biomimetics*. 2019; 4(4):77.
https://doi.org/10.3390/biomimetics4040077

**Chicago/Turabian Style**

Godoy-Diana, Ramiro, Jérôme Vacher, Veronica Raspa, and Benjamin Thiria.
2019. "On the Fluid Dynamical Effects of Synchronization in Side-by-Side Swimmers" *Biomimetics* 4, no. 4: 77.
https://doi.org/10.3390/biomimetics4040077