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Soft matter and liquids

Soft matter and liquids

Invisibility cloak for water waves

02 Oct 2008
Cylindrical cloak for water waves

It should be possible to protect coastlines from tsunamis by making the land invisible to the incoming waves. That’s the claim of a group of physicists in France and the UK, which has built a cylindrical “invisibility cloak” that shields objects from water waves by directing those waves around the object as if it weren’t there.

Researchers have already built so-called invisibility cloaks to shield objects from electromagnetic radiation. Two years ago a group led by David Smith at Duke University in North Carolina demonstrated a how a cylinder built from artificial materials known as metamaterials can make an object almost invisible to microwaves, by steering the waves around the object as if those waves had propagated forward without interruption.

That concept has now been extended to water waves by Stefan Enoch of the University of Aix-Marseille and colleagues. Enoch’s colleague, Sebastien Guenneau of Liverpool University, explains that the mathematics behind the invisibility cloak involves a geometric transform – which takes a point, inflates it and renders anything that lies inside the resulting bubble unreachable by the waves — which holds true for water waves just as does for electromagnetic waves.

Works just like a whirlpool

The cloak built by the French-UK team is a shallow metal cylinder, measuring 10 cm across. The cylinder does not have solid walls but instead consists of a series of rods arranged in 100 identical sectors and seven concentric rings (Phys. Rev. Lett. 101 134501 ). Guenneau says that the object functions just like a whirlpool, and indeed generates the same solutions to the Navier-Stokes equations of fluid dynamics as a whirlpool does.

The liquid enters through the gaps between the rods (ie. from the side of the cylinder), swirls around the concentric rings and then enters the far side of the cylinder so as to leave the central region entirely free of liquid. The trick, says Guenneau, is to transform the waves so that they have a greater velocity along the circumference of the rings than along the radii, therefore slowing down the liquid as it approaches the centre and forcing it out the far side. “We are encouraging waves to travel in non-Euclidean space,” he says. “To travel in curved trajectories rather than straight lines.”

To demonstrate their invisibility cloak, Enoch and colleagues filled a tank with the liquid methoxynonaflourobutane and then created waves along the surface of the liquid by sending pulses of air through a tube located on one corner of the tank. They were unable to use water in their experiment because it is too viscous and would have got stuck between the tiny rods. And even then they were limited by the size of their tank to recording the reduction in diffracted waves on the near side of the cloak [see figure 3 left and right in the paper], but they say that numerical simulations prove the cloak would have reconstructed the waves on the far side as predicted if their tank had been big enough.

Protecting coastlines

Although the effects of viscosity prevented the team from demonstrating their device in water, Guenneau points out that this problem no longer holds when on larger scales such as coastlines (indeed, he says cloaks as small as a metre in diameter should demonstrate the effect). He believes that authorities could build one half of a cloak around a beach or other stretch of coastline that needs protecting from dangerous waves, in order to bend the waves around that bit of coast. He points out that this would be preferable to simply breaking the waves by building a dyke as waves’ amplitude increases when they break, leaving the beach vulnerable when the sea level rises significantly.

He does, however, concede that people building protective invisibility cloaks would need a certain amount of faith that a series of posts would protect them more effectively than a solid wall. “You have to believe in Navier-Stokes,” he adds.

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