Catch a glimpse of a fish's body shape, and you can often guess which is the speediest. Tuna and mackerel look as if they should outpace frilly reef fish and eels. But how have all of these diverse body shapes evolved? Have fish bodies been shaped by the hydrodynamics of their environment or did they evolve for other reasons? However, answering this question with real fish is almost impossible. ‘It is very difficult to control real fish, you can't tell them what to do and a mackerel will always swim like a mackerel,’ explains engineer Fotis Sotiropoulos. So he turned to computational fish: they are much more cooperative and adaptable. ‘They allow you to explore scenarios that real fish could not,’ says Sotiropoulos: such as how would an eel-shaped fish that swam like a mackerel perform in a race with a mackerel swimming like a mackerel? Curious to find out how much of an influence hydrodynamics has had on fish shape and swimming styles, Sotiropoulos and colleague Iman Borazjani from the University of Minnesota decided to race hybrid and realistic fish in a massive parallel computer cluster to find out what influence the aquatic environment has had on fish shapes and swimming techniques (p. 89).

But building the computational fish was far from straight forward. ‘We started this work over 5 years ago,’ says Sotiropoulos, and adds ‘it was a challenge because we had never simulated anything living before’. Having developed the algorithm, the duo was able to control the computational fish's tail beat frequencies and the viscosity of the fluid around the fish to see how they performed under different conditions.

But why vary the viscosity of the fluids in the computational ponds? Borazjani explains that the hydrodynamic forces exerted on swimmers vary enormously depending on their size and speed. Slow tiny swimmers (like sperm and bacteria) are held back by viscosity, while medium fast swimmers (eels) experience viscous forces and their own inertia. However, the fastest swimmers (mackerel) are hardly affected by fluid viscosity: the main force that affects them is inertia. Knowing that mackerel and eels swimming in water experience different hydrodynamic environments, the duo simulated these different environments by varying the computational fluid's viscosity.

Building two computational mackerels (one that beat its tail like a mackerel and a second that wiggled like an eel) and two eels (one that wiggled and another that beat its tail like a mackerel), the engineers set the fish racing from standing starts and waited to see how they performed.

Analysing the race results from medium speed hydrodynamic conditions, it was clear that no matter whether the fish was shaped like an eel or a mackerel, the winner always used the eel-type wiggle. However, for races swum under high-speed hydrodynamic conditions the winner always used the mackerel tail beat, even if it was shaped like an eel. So the real mackerel and eel's swimming styles are perfectly adapted to the hydrodynamic environments that they inhabit.

The duo also measured the fishes' efficiencies. The mackerel body shape was the most efficient in the high-speed hydrodynamic conditions while the eel shaped swimmers were most efficient in the medium fast environment. Finally the duo calculated the wake structure generated by the computational fish and realised that many of the features that they found in the wakes of the mathematical fish are produced by real fish when they swim. ‘Even though we have stripped down the fish to their basic shapes and removed some degrees of freedom, we still had enough of the physics there to reproduce these experimental findings,’ says Borazjani.

But what do the duo's calculations tell us about the influence that the aquatic environment has had on fish forms and swimming styles? ‘We can deduce that each particular shape and swimming mode is consistent with the hydrodynamics of the regime they swim in. It is significant evidence that there is a link,’ says Sotiropoulos.

On the role of form and kinematics on the hydrodynamics of self-propelled body/caudal fin swimming.
J. Exp. Biol.