November 30, 2023
Law of disappearance of water waves

Law of disappearance of water waves

Physical 16, 196

Cavities in the sides of a water channel can cause waves to be completely absorbed, suggesting new techniques for protecting the coastline.

Goodbye wave. This conceptual view shows a waveguide directing water waves to pass through two cavities. These cavities, for a given choice of dimensions, can generate secondary waves that completely cancel the reflected and transmitted waves, demonstrating perfect absorption (see image below).

If waves of water, light, or sound collided with a hypothetical object called a perfect absorber, they would neither be reflected nor transmitted; they would simply disappear. Researchers have now demonstrated perfect absorption using ordinary water waves traveling through a narrow channel [1]. The waves are canceled out by their own reflections in the cavities built into the side of the channel. With further development, researchers believe the effect could be used to reduce erosion or protect sensitive structures, using a series of elements deployed close to the coast.

“We were motivated by the need to control or absorb waves in rivers or to protect coasts,” says mathematical physicist Agnes Maurel of ESPCI Paris. “Completely absorbing wave energy is even better than redirecting it, and you can also imagine perhaps harvesting that energy.”

But achieving perfect absorption is not easy. In recent years, researchers working with light or sound waves have demonstrated something very close to perfect absorption. But no one has created a perfect absorber for water waves.

Maurel and his colleagues were inspired to try a new approach based on their own recent mathematical work, which showed that perfect absorption could be achieved by engineering a particular type of resonant structure with which incoming water waves would interact. [2]. This work showed that for waves traveling through a straight channel, these structures, when excited by a passing wave, would radiate secondary waves that would perfectly cancel out waves going both forward and backward.

Without leaving a trace. In this image from the experiments, the waves arriving from the left disappear when they reach the pair of cavities.

To demonstrate this theory in practice, Maurel and his colleagues followed a two-step procedure: they first analyzed how the cavities could produce zero transmission at specific frequencies, and then tuned this configuration to produce zero reflection at those same frequencies. They considered a water channel 1.4 m long, 6 cm wide and 5 cm deep. In preliminary calculations, starting from the equations for an ideal fluid – without energy losses due to friction – they showed that two small cavities built into the side of the channel could act as the necessary resonant chambers. These calculations assumed that the two cavities were of identical size, extending from the canal wall by 4 cm and extending along the canal by 3 cm. For waves in the frequency range the team studied, these calculations predicted zero transmission at 2.7 and 3.3 Hz.

The team then tested these predictions with water waves in the laboratory. In close correspondence with predictions, the researchers found two dips in the transmission versus frequency curve – the first almost reaching zero and the second falling to around 40%. The discrepancies with theory, the researchers say, reflect frictional losses in the fluid and the approximations used in the analysis.

This arrangement did not produce perfect absorption at either frequency because reflection was significant. But researchers discovered that by distorting the two cavities, making one extend slightly further from the channel wall than the other, they could achieve perfect absorption – zero transmission and reflection – at 2.9 Hz. Doing so required some trial-and-error adjustment of the precise asymmetry of the cavity in order to make the zeros in transmission and reflection appear at precisely the same frequency.

Maurel and colleagues hope to develop this idea for use in a practical system to protect coastal areas from erosion. “The mechanism we demonstrated for guided waves can be extended to a kind of protective belt at sea,” she says.

“This is an important paper,” says Sébastien Guenneau, from Imperial College London, an expert in wave propagation in a wide range of applications. “The two closely spaced water cavities talk to each other and act like pistons in an engine” because their water levels tend to oscillate just out of phase. He foresees applications such as “new types of dikes that can contain water with reduced risk of overtopping”. And he says resonant structures could also be used to harvest energy from ocean waves.

–Mark Buchanan

Mark Buchanan is a freelance science writer who divides his time between Abergavenny in the UK and Notre Dame de Courson in France.


  1. L.-P. I see and others.“Perfect resonant absorption of water waves guided by the Autler-Townes split,” Physical. Rev. 131204002 (2023).
  2. R. Porter and others.“Modeling the Autler-Townes splitting and acoustically induced transparency in a waveguide loaded with resonant channels,” Physical. Rev. 105134301 (2022).

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