Proposed Cloaking Device for Water Waves Could Protect Ships at Sea
Underpass. Appropriately sculpted ripples on the ocean floor could convert surface waves into internal interfacial waves, allowing them to pass under a floating object and protecting the thing from jostling.
Credit: M.-R. Alam, PhysRevLett, 108 (24 February, 2012)
The weird science of invisibility has entered uncharted waters. By altering the sea floor in just the right way, it should be possible to hide an object floating on the sea from passing waves, a fluid mechanician predicts. The technique might help to protect ships and floating structures from rough seas. And because the scheme works entirely differently from the "cloaks" developed to hide objects from light and other electromagnetic waves, it breaks new ground for research.
"This is great fun and a brilliant idea," says Ulf Leonhardt, a theoretical physicist at the University of St. Andrews in the United Kingdom.
In ordinary cloaking, the idea is to smoothly funnel light around an object so it emerges on the other side of the object as if nothing had been there. The basic theory behind that approach is called transformation optics. It envisions literally bending space and time so that light will flow around the object. The theory then shows how to simulate that warping of space and time by surrounding the object with a "cloak" with precisely tuned optical properties. The cloak consists of an assemblage of metallic rods and rings known as a metamaterial. Since 2006, researchers have fashioned rudimentary invisibility cloaks for radio waves and even for light.
Now, Mohammad-Reza Alam, a fluid mechanician at the University of California, Berkeley, has come up with a different method that, in principle, can cloak an object floating on the sea such as a buoy or an oil-drilling rig from water waves rippling across the surface. To begin, Alam notes that the ocean water tends to separate, or "stratify," into two layers: a colder, denser layer below and a warmer, lighter layer above. And just as waves can zip across the surface of the water, they can also ripple along the interface between the layers. Alam's idea is simple: As a surface wave approaches an object, transform it into an interfacial wave that will pass beneath the object. Then, once the interfacial wave has passed the object, transform it back into a surface wave. (See figure.)
To make that happen, Alam takes advantage of a key difference between the surface waves and the interfacial waves. For the same frequency of oscillation, the interfacial waves will have a much shorter wavelength and lower speed than the surface waves above. That makes it possible to transfer energy from the surface wave to the interfacial wave by placing a patch of wavy ripples on the sea floor in front of the object that have a wavelength that's tuned just right. The precise condition is easiest to understand in terms of "wave vector," essentially one over the wavelength: The wave vector of the ripples must equal the difference in the wave vectors of the interfacial and surface waves.
The energy transfer takes place because both types of waves "feel" the bottom, Alam says. And a second, identical patch of ripples on the other side of the object turns the interfacial wave back into a surface wave. Alam demonstrates the technique with computer simulations in a paper published 23 February in Physical Review Letters. To make a cloak for multiple wavelengths of surface waves, one need only add multiple patches on the sea bottom, he reports in the paper.
Could such a simple idea have real-world applications? Quite possibly, says Marc Perlin, a fluid mechanician at the University of Michigan, Ann Arbor. "This thing would work, I think, to protect offshore structure," Perlin says. "I think it has a lot of potential."
Of course, as Perlin notes (and Alam acknowledges in the paper), the real sea is much more complicated than the idealized model in the analysis. For example, it generally has a gradient of density, not two definite layers. And the surface ripples with many waves of various wavelengths and not just waves of one wavelength. However, those factors would likely only reduce, not eliminate, the effectiveness of the device, Perlin says. Even an imperfect cloaking device that didn't completely squelch surface waves could still be useful, he says. "If they wanted to use it to provide a zone for protecting fishing boats, a zone to huddle in, then it might work," Perlin says.
The new scheme works only in the context of layered seas, Leonhardt notes. Nevertheless, it provides a wholly new take on cloaking, he says. "It's more limited [than transformation optics]," he says. "But on the other hand, it's a new twist on the idea of cloaking and could inspire others to pursue other new directions."