Eels are endurance swimmers. For example European eels migrate to Europe from their spawning grounds in the Sargasso Sea in the North Atlantic Ocean and return again at the end of their lives. The animals accomplish this “last journey” of 6000 kilometres without eating because their digestive system atrophies. So it has long been assumed by biologists to be clear that the sinusoidal propulsion that these animals use must be very efficient. However, a detailed study in an aquarium of the eels’ movement yields a contradictory picture: the astonishing result is that the eel does not seem to manage its strength very economically when swimming. Stefan Kern and Petros Koumoutsakos of the ETH Zurich Institute for Computational Science have now been able to use a three-dimensional computer simulation to show that there is no contradiction between biologists’ assumption and the Institute of Computational Science’s own study. (1) On the contrary, the eel uses different swimming modes depending on the situation.

Evolutionary algorithm

The computer model did not define the body movement a priori but determined it with an evolutionary algorithm based on Darwin’s “Survival of the fittest” principle. The model uses a set of parameters to describe the animal’s movement pattern. In a first step the computer defines a population of animals having different parameters. Next the program selects the most successful animals as the parents of the following generation. The selection cycle is repeated until a stable population is established. The only selection criterion specified at the outset was that the animals should swim either particularly fast or in a particularly energy-efficient way.

The calculations now show that the outcome is a completely different movement depending on the pre-defined specification. If an eel wants to swim as fast as possible, for example to avoid capture or when hunting, it keeps the front part of its body straight and moves only its tail. On the other hand animals that want to swim as efficiently as possible employ the whole body, making the typical sinusoidal movement. The difference between the two swimming modes is remarkable: an eel moves forward 40 percent faster by using tail movement than when it moves its entire body. However, it pays a high price for this: believe it or not, the efficiency is 60 percent lower compared to calm sinusoidal movement.

ETH Zurich researchers were able to use their model to show which kind of eddy flow occurs in water when an eel propels itself forward with a typical sinusoidal movement. The different colours show the intensity of turbulent flow. The image of the animal itself is white and can be seen through the envelope in the front part of the graphic. large

A variety of possible applications

The calculation and optimisation methods that were used can also be applied to other modes of swimming or to novel propulsion systems, for example to the swimming zeppelin (2) being developed by the Swiss Materials Research Institution (EMPA) at Dübendorf. Eel-like movements also feature in the sustainable generation of electric power using wave energy power plants (Pelamis) (3).

In collaboration with Kristina Eschler of the School of Art and Design Zurich, the results were summarised in an animation that won an award from the Gallery of Fluid Motion of the American Physical Society (APS). (4)