Take a stroll on the beach and you might spot a mini-tsunami ? if you know where to look. Once thought to be extremely rare, X- and Y-shaped waves with unusually high peaks regularly appear in ankle-deep water under certain conditions.
The discovery should help improve mathematical models of these non-linear waves, including the larger-scale versions that may give rise to particularly devastating tsunamis.
Linear interaction between ocean waves creates a peak that cannot be greater than the sum of the individual wave heights. But X- and Y-shaped waves are created when two waves hit each other at an angle, causing a non-linear interaction. That means their combined height can be more than the sum of the original peaks.
The existence of these oddly shaped waves had long been predicted by mathematicians studying equations for shallow-water waves. However, their non-linear interactions make it difficult to model the phenomenon without real-world observations, and until recently, such waves had been photographed only once ? in the 1970s.
"People thought you might see them once every few years. The surprise is that they occur every day," says Mark Ablowitz, a mathematician at the University of Colorado, Boulder.
Wave spotting
Ablowitz first spotted the waves while on holiday with his family in Nuevo Vallarta, Mexico, in 2009.
"All of a sudden, we hit that few-minute period and we saw them," he says. "My children and my wife saw them, and we were all starting to point. People thought we were crazy."
Since then, Ablowitz has recorded many more examples in Mexico, while his colleague, Douglas Baldwin, has captured them in Los Angeles, California.
The new work shows that X- and Y-shaped waves occur most frequently shortly before or after low tide on flat beaches and that they are more likely to appear near jetties, which help create cross-waves.
Full stem
Detailed observations of these waves could help explain how similar non-linear effects give rise to especially powerful tsunamis.
Not all tsunamis are boosted by wave interactions, but when they are, the results can be catastrophic. For instance, satellite photographs of the 2011 Japanese tsunami show an X-like structure beneath the surface, Ablowitz says.
"In that case, the X was close to the shore, so it didn't have time to develop a full stem," he says. "We know mathematically that a full stem could be up to four times larger. Had it been further away, it could have developed more significantly and been even more devastating."
Simon Boxall of the National Oceanography Centre in Southampton, UK, says the new photos and videos offer an alternative view of the interactions behind tsunamis that cannot be achieved artificially.
"It is very difficult to recreate the ocean in the laboratory, so often we're reliant on the real world," he says.
Journal reference: Physical Review E, doi.org/jc9
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