When fish swim in schools, they conserve energy by synchronising the movement of their tail-fins.

The caudal - or tail - fin provides the power needed to propel a fish forward; it also acts like a rudder to help it steer.

Now, researchers from Tohoku University in Japan have developed a model that simulates this motion, uncovering the underlying mechanisms behind this commonly observed phenomenon. They say the discovery could support developments in robotics and drones.

In fluid dynamics, a Kármán vortex is the name given to swirling currents that form behind an object moving through liquid. In reverse, the vortices rotate in the opposite direction. It is the synchronisation of the movement of fishes' tail fins that creates vortices that others in the school can ride, saving energy.

"A long-standing hypothesis about swimming fish is that they exploit the vortex flow generated by other fish to save energy," explains physicist Susumu Ito. "They work in tandem to utilise the reverse-Kármán vortex street and adjust their caudal fins accordingly."

To find out more about these mechanics, the researchers developed a unique theoretical model that considers not only the regular muscle-driven movements of fish, and the impact of the forces of the water, but also natural variations in physiological factors that can affect how fish move. This meant the model could mimic the way fish naturally coordinate their actions in more detail.

Energy reduction

After running numerical simulations, Ito and his team were able to replicate the synchronisation of caudal fins and demonstrate that it results in a significant reduction in energy dissipation for a pair of fish at distances shorter than half a body-length. However, the results also suggest that the typical timing of fin movements between two fish does not lead to the most optimal means of conserving energy.

The model also applies to various fish species that swim with a carangiform style - where only the rear of the fishes body flexes - such as horse mackerel, trout, salmon, carp and goldfish.

"We have illuminated the dynamics of synchronisation in biological species, which can also be applied to other living creatures such as birds, animals, bacteria, and even unicellular eukaryotes," said Ito. "The benefits extend to robotics too; the discovery could help find new energy-saving strategies for groups of drones moving in coordination."

Details of the research were published in the journal Physics of Fluids.