Maths explains rogue waves
A rogue wave photographed in the Bay of
Image: US National Oceanic and
Atmospheric Administration.

The mystery of why there are ‘rogue waves’ on the world’s oceans is one step closer to being solved thanks to a team of optical scientists from ANU.

The team, led by Professor Nail Akhmediev of the ANU Optical Sciences Group, has been using mathematical concepts to try and shed light on rogue waves – one of the great mysteries of the deep sea. Until quite recently, rogue waves were regarded as fanciful sea tales where ships were engulfed by one-off waves with a massive wall of water. Recent studies from the European Union have shown that they do exist, and now the ANU team has shown how.

Although Professor Akmediev’s team are working to improve optical devices, it occurred to them that the mathematical equations they used in the field of non-linear optics could be applied to explaining rogue waves in the ocean.

“Waves on the ocean and light beams may seem like totally different things, but the underlying mathematics is almost exactly the same,” said Professor Akhmediev. “There’s no reason why models based on mathematical concepts like the nonlinear Schrodinger equation can’t work as well for water as they do for light and quantum wavefunctions.”

The solution the team have come up with to explain rogue waves sees two waves amplified by nonlinear effects occur at the same time purely by coincidence. This leads to further nonlinear behaviour, resulting first in a great hole appearing in the water, followed by a massive peaked wave many times higher than the average wave height in local conditions.

They hope that this discovery will help scientists to learn more about where these rogue waves might appear.

“There are so many variables that the behaviour of ocean waves is a highly chaotic system. So although there are conditions like bad weather and current flows that increase their probability, when and where they appear is largely just a matter of chance,” said Professor Akhmediev.

“But this doesn’t mean it’s hopeless. You never know what will happen in the future. Maybe now we understand what’s going on, one day it might be possible to predict or even disrupt such waves as they begin to form near ships.”

Editor's Note: Original news release can be found here.