Universal Scaling Laws for a Generic Swimmer Model

TL;DR

This paper introduces a minimal, force-based swimmer model that accurately reproduces propulsion across various Reynolds numbers and derives universal scaling laws validated by experimental data, aiding large-scale collective flow simulations.

Contribution

The paper presents a simple, generic swimmer model capable of simulating propulsion and wake vortices across flow regimes, and derives universal scaling laws validated by experimental data.

Findings

Model reproduces swimmer propulsion from low to high Reynolds numbers.

Derived universal scaling laws match experimental data across regimes.

Model enables efficient simulation of collective effects in fish schools.

Abstract

We have developed a minimal model of a swimmer without body deformation based on force and torque dipoles which allows accurate 3D Navier-Stokes calculations. Our model can reproduce swimmer propulsion for a large range of Reynolds numbers, and generate wake vortices in the inertial regime, reminiscent of the flow generated by the flapping tails of real fish. We performed a numerical exploration of the model from low to high Reynolds numbers and obtained universal laws using scaling arguments. We collected data from a wide variety of micro-organisms, thereby extending the experimental data presented in (M. Gazzola et al., Nature Physics 10, 758, 2014). Our theoretical scaling laws compare very well with experimental data across the different regimes, from Stokes to turbulent flows. We believe that this model, due to its relatively simple design, will be very useful for obtaining numerical simulations of collective effects within fish schools composed of hundreds of individuals.