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Geometric ideas and concepts

Jet-Propelled Tuna

by Bennett Daviss
New Scientist, March 4, 2000

For the first time, we have a good model of how fish swim; in the unlikely shape of an aluminium skeleton that turns flapping into an art form. Bennett Daviss reports

"THIS," says Michael Triantafyllou reverently, "is a tuna." He thrusts an object the size of a four-year-old child into the arms of a visitor to his lab. It isn't a real tuna, just a fibreglass cast, but Triantafyllou's enthusiasm for its streamlined form almost brings it to life.

He conducts a nose-to-tail tour of the fish that most biologists nominate as nature's most efficient swimmer. He points out the shallow depressions in the tuna's body into which it can fold its pectoral fins to reduce drag. He explains the way that the long, serrated fin that runs from its belly to its tail can subtly direct water flow to ease the fish forward. "Nature has spent millions of years perfecting this design," he says. And if it's good enough for nature, it's good enough for Triantafyllou.

Since 1992, this naval architect and professor of ocean engineering at the Massachusetts Institute of Technology has been trying to teach machines to swim like fish. He envisions fleets of tuna-shaped robots criss-crossing the oceans for days or weeks at a time, mapping nutrient concentrations or temperature gradients. Meanwhile, robotic pike-modelled on the fish famous for its astounding acceleration-could reconnoitre dangerous spots around volcanic vents or chemical spills. And Triantafyllou imagines a mechanical muskellunge, based on the agile North American gamefish, twisting and turning among underwater wreckage while human observers watch from the safety of a support vessel via an on-board camera.

As Triantafyllou and his colleagues have been transforming these dreams into reality, they have also been busy using their robots to solve the mystery of how fish swim so efficiently. What they have learnt is remarkable. It seems fish manipulate the water around them, drawing energy from whirling vortices not just to turn on a sixpence, but also to swim faster than their muscles alone could propel them.

Triantafyllou's mission grew out of controversial research by physiologist James Gray. In 1936, Gray calculated that fish shouldn't be able to swim-at least not nearly as well as they do. At that time, dolphins were thought to swim at speeds of up to 10 metres per second, but Gray's experiments suggested that their muscles couldn't move them this fast. Fish, Gray concluded, must somehow manipulate water to ease their passage through it. Although scientists now believe that Gray's calculation was flawed, his belief that fish can control the flow of water around them has continued to intrigue (New Scientist, 20 November 1999, p 28).

Fish and ships

It was this question that first caught the attention of Triantafyllou and his brother George, who is also a naval engineer. They were hoping to find new ways to make ships more efficient, and began by pondering a fish's chief source of power-its tail. They reasoned that the tail had to be particularly good at moving water, and that something similar attached to a boat should boost speed and save fuel. However, when they tested simple foils that swished like fishtails, the models squandered energy.

So the brothers began to look at one of the basic principles of fluid dynamics. Any object in a flow-a rock in a stream, an airplane wing in air, or a fish in water-leaves trails of eddies or "vortices" behind it. A rigid object like a sailing boat obstructs the flow and leaves a swirling wake as it cuts through the water, but when a fish swishes its tail it actively pushes water backwards. The result isn't a simple wake but a jet of moving water. The researchers had a hunch that the vortices inside this jet somehow generate thrust. If they were right, then the key to boosting the efficiency of their foils should be to manage these vortices deftly.

In earlier studies of vortices, the brothers had encountered something called the Strouhal number. By multiplying the width of an object's wake by the frequency with which vortices form inside it, then dividing the result by the speed of the flow, the Strouhal number gives a measure of how fast vortices are being created and how close together they are.

Working with Mark Grosenbaugh, a marine engineer at the Woods Hole Oceanographic Institution in Massachusetts, the researchers decided to apply the equation to swimming fish. They adapted the Strouhal number to express the frequency of tail swishes multiplied by the width of the jet, with the product divided by the fish's forward speed. Then they retreated to their lab and flapped their foils at a range of speeds and amplitudes. Measuring the results and refining the combinations, they found that the foils moved the most water using the least amount of energy when the Strouhal number was between 0.25 and 0.35. In that range, their fabricated fishtails delivered efficiencies of up to 86 per cent, compared with a maximum of about 80 per cent for the peak efficiency of ships' propellers. Later, they discovered that most fish swim within that same range-far above the 0.1 or less that the Triantafyllous' earlier foils had struggled to achieve.

They decided that the only way to learn how these creatures accomplish this apparently impossible task was to build their own aquatic robot. So over the next two years, the Triantafyllous and Grosenbaugh worked with graduate student David Barrett to meticulously copy the external physiology of the bluefin tuna, the creature that many zoologists believe is the most efficient swimmer in the oceans.

To do this, they built a body with eight jointed sections and an intricate system of pulleys and strings-the mechanical equivalent of muscles and tendons-to make it move on command. In 1994, the RoboTuna was finally baptised in the MIT test tank (New Scientist, 1 October 1994, p 22).

All the robot's movements are programmed into an external computer and effected via cables in a rigid mast attached to the top of RoboTuna's head. As the mast tows the automaton through the water, the computer moves the body sections in predetermined ways and the sensors transmit water-pressure data back to the computer. As the apparatus moves, Michael Triantafyllou and his team watch to see what happens to the water around the fish using a technique called digital particle imaging velocimetry.

To set up the experiment, tiny fluorescent particles that are neutrally buoyant are added to the water in the test tank. The lab is darkened and the robot begins to swim the length of the tank. As it moves, two laser beams-each spread into a two-dimensional sheet of light with a special lens-flash alternately. These horizontal sheets of laser light slice through the water in the plane in which the robot is swimming, lighting up the fluorescent particles. A video camera looking down into the tank takes a picture every time a laser flashes and the researchers use these images to track the luminescent particles. From this, they can work out the movement of water around the fish.

The researchers then analyse those patterns and combine them with water pressure readings to determine which combination of body movements-tail-flapping frequencies, flapping amplitude and body flexing-yield the smoothest flow of water and, therefore, the greatest efficiency.

However, there is an almost infinite number of ways to combine the frequency and amplitude of tail movement with the positions of eight body sections. To sort through those permutations relatively quickly, the team used a genetic algorithm-a sort of digital breeding programme.

RoboTuna would test 10 combinations of these properties in succession. Then a computer sorted through the data to rank the patterns of body and tail motions according to their efficiency. Trials ranked in the bottom five were discarded. Then those that remained were "cross-bred" and retested. Again, the least efficient were discarded and the survivors cross-bred. In total, about 2000 digital offspring were produced, speeding up-perhaps by years-the work of discovering the most efficient combination of motions.

After this programme, the researchers believe they have a pretty good idea of how fish swim so efficiently. It's not just a fish's tail that matters: the role played by the rest of its body turns out to be far more important than almost anyone suspected.

Hints that this might be the case first surfaced in 1973. In a strange experiment, a biologist called Paul Webb who was working at the University of Michigan at Ann Arbor amputated the tails of young salmon, threw them back in the water and found that they still delivered about 80 per cent of their swimming efficiency. No one really understood how this could be, and the finding was forgotten.

Until recently, that is. In September 1999, in a paper published in The Journal of Experimental Biology, Grosenbaugh and Triantafyllou not only confirmed Webb's result, they also explained what was behind it: they found that it is the body of a fish, rather than its tail, that creates the strongest vortices in the water.

In a spin

As a fish swims, undulations in its body create differences in water pressure that help to pull the fish forward, much as the curves on the surfaces of an airplane's wing create a difference in air pressure that allows the plane to rise into the air. But these movements also stir the water around the fish, whipping up a series of large vortices, one after another. Depending on the way the fish wiggles, some of the vortices rotate clockwise, others anticlockwise. As the fish moves forward, these vortices roll along the fish's body and into the path of its tail.

That could spell trouble. Depending on their direction of spin, some of the vortices throw water back toward the fish. That might seem useful, like having a tailwind.

In reality, it creates chaos. If these vortices simply fell directly behind the fish, they'd send water crashing into the wake that the fish is creating with its tail. The result would be a drag-inducing backwash.

However, the researchers have shown that fish have evolved a clever trick to avoid this. As the vortices trail off the body at the tail, they roll up into bundles. "The vortices swirl around each other and wrap up together," says Grosenbaugh. The fish seems to sense the direction in which each is spinning. With flicks of its tail, it sweeps each bundle of vortices spinning clockwise towards the left and anticlockwise ones to the right. When these vortices meet behind the fish, they form a jet that sends water away from the fish, boosting thrust just as a jet engine sends hot gases backward to propel an airplane forward (see Diagram).

Fish exhibit a similar level of control when it comes to changing direction. Just as some jet aircraft can use thrust vectoring to manoeuvre quickly, the body and tail of a fish combine to create a sudden, directed spurt of water from a pair of counter-rotating vortices which spins the fish around on the spot. Remarkably, the researchers found that the fish sheds no uncontrolled vortices as it turns. "We were the first to show this large vortex structure around the fish body," says Grosenbaugh, "and to explain how the body uses it to perform so well on its own."

Triantafyllou believes that a fish does a similar trick with smaller vortices formed along its sides by its forward motion. As a fish swims, the water molecules that it touches are dragged along with it. This sets up microscopic vortices in a thin layer of water along the fish's body. These tiny eddies create friction or drag that should slow the fish down. But Triantafyllou has a hunch that fish may even be able to recapture this small stream of lost energy.

The fish's tail could never move fast enough to swish this continuous stream of tiny whirlpools from one side to the other. So Triantafyllou suspects that as these vortices roll off the fish, they, too, tangle together to form large vortices that the fish can control easily. If he's right, the fish could recapture much of the energy that its body loses as friction. "It's possible that the fish does something with these microscopic vortices," Grosenbaugh admits. "We need to do more work."

While Grosenbaugh pursues those basic questions, Triantafyllou is awaiting further funding that will send his creations into the open sea. His group has crafted a free-swimming robotic pike and muskie, whose movements are preprogrammed to keep their efficiency in the optimal range (New Scientist, 28 February 1998, p 11). At the same time, the team is building a second-generation RoboTuna to include a feedback system that will continually adjust body and tail motion to maximise efficiency as water conditions change. And as the feedback system evolves, its adaptations will be built into the pike and muskie.

Descendants of Triantafyllou's robofish with the ability to think for themselves could survey the seabed in hazardous zones such as thermal vents, or monitor the condition of underwater equipment such as oil and gas rig structures and optical fibre cables. At least that's the vision of William Sandberg, deputy director of the Laboratory for Computational Physics and Fluid Dynamics at the Naval Research Laboratory in Washington DC. Robotic fish could even conduct underwater damage assessment for ships at sea. "There are many inherently dangerous missions they could perform that now require sending down expensive, multipurpose vehicles-if the vehicles are even available-or risking the safety of humans," says Sandberg.

Even though they're still only swimming around in tanks, Triantafyllou's current generation of robots have turned out to be more useful than anyone expected. "This is the first work I know of that models the comprehensive motion of fish," says Mory Gharib, a specialist in biofluid mechanics at the California Institute of Technology in Pasadena. "It's almost impossible to create a computer model-there are just too many possible combinations. The only way to figure it out is to build a physical model or run experiments. Their project does both, which is best because that way you learn directly from nature."

Further reading:
: Near-body flow dynamics in swimming fish by M. J. Wolfgang, M. A. Grosenbaugh, M. S. Triantafyllou and others, The Journal of Experimental Biology, vol 202, p 2303 (1999) For more information see:

From New Scientist magazine, vol 165 issue 2228, 04/03/2000, page 36

Copyright New Scientist, RBI Ltd 2000

Bennett Daviss is a freelance technology writer based in New Hampshire
Raising a Stink
New Scientist, June 6, 2000, vol 166 issue 2241, page 4

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