Laboratory experiments show that obstacles arranged in fluids in certain patterns can effectively make objects they surround invisible to waves. If it works as well in in scaled-up versions, it could lead to new ways to protect ocean-based platforms and coasts from devastating tsunamis. Credit: M. Farhat, S. Enoch, S. Guenneau and A.B. Movchan
Rather than building stronger ocean-based structures to withstand tsunamis, it might be easier to simply make the structures disappear. A collaboration of physicists from the Centre National de la Recherche Scientifique (CNRS) and Aix-Marseille Universite in France and the University of Liverpool in England have conducted laboratory experiments showing that it’s possible to make type of dike that acts as an invisibility cloak that hides off-shore platforms from water waves. The principle is analogous to the optical invisibility cloaks that are currently a hot area of physics research.
This paper describes transport properties of linear water waves propagating within a square array of fixed square cylinders. The main focus is on achieving the conditions for all-angle-negative-refraction (AANR) thanks to anomalous dispersion in fluid-filled periodic structures. Of particular interest are two limit cases when either the edges or the vertices of the cylinders come close to touching. In the former case, the array can be approximated by a lattice of thin water channels (for which dispersion curves are given in closed form and thus frequencies at which AANR occurs) whereas in the latter case, the array behaves as a checkerboard with cells consisting either of water tanks or rigid cylinders (for which standing modes are given in closed form). The tools of choice for the present analysis are, on the one hand, the finite element method which solves numerically spectral problems in periodic media, and on the other hand, a two-scale asymptotic method which provides estimates of dispersion curves and associated eigenfields through a lattice approximation (namely thin water channels between rigid cylinders). Simple duality correspondences are found based on fourfold symmetry of square water checkerboards that allow us to get some insight into their spectra. Last, some numerical evidence is provided for water waves focusing with no astigmatism through such arrays, when they are of finite extent.
Tsunami invisibility cloaks wouldn’t make structures disappear from sight, but they could manipulate ocean waves in ways that makes off-shore platforms, and possibly even coastlines and small islands, effectively invisible to tsunamis. If the scheme works as well in the real world as the lab-scale experiments suggest, a tsunami should be able to pass right by with little or no effect on anything hidden behind the cloak
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