In a study published in Physical Review Letters, researchers from Université Grenoble Alpes introduce a swimmer model that replaces the complex details of fins, flippers, and undulations with a simple combination of force and torque dipoles — the basic ingredients of movement in fluid. Despite its simplicity, the model successfully replicates swimming behavior across a vast spectrum of Reynolds numbers (a measure of inertial versus viscous forces), from sluggish microbial motion to turbulent fish propulsion.

The team’s simulations, powered by full 3D Navier-Stokes fluid dynamics, not only reproduce characteristic flow features like vortex wakes seen in swimming fish, but also uncover universal scaling laws linking the swimmer’s speed, size, and force production. These laws neatly categorize swimming into three regimes: Stokes (slow, viscous), laminar, and turbulent, and match remarkably well with hundreds of experimental data from real aquatic animals and micro-organisms. Importantly, the study introduces a new dimensionless "thrust number" that captures the physical forces behind swimming and predicts swimming efficiency across all scales.


“Our model shows that despite differences in shape or swimming style, all swimmers obey the same basic physics,” says the first author, Bruno Ventéjou. “This paves the way for large-scale, accurate simulations of animal groups in motion, like fish schools or microbial swarms.”

By stripping aquatic motion down to its essentials, this model offers a powerful tool for analyzing swimming and designing efficient bio-inspired robots.