Monster waves are more than just mariners’ tales

That’s Maths: Rogue waves appear to have more than a single cause but their precise origin remains a mystery

In January 2014, a rogue wave higher than 29m was measured off Killard Point in Co Clare in water 40m deep. photograph: thinkstock

In January 2014, a rogue wave higher than 29m was measured off Killard Point in Co Clare in water 40m deep. photograph: thinkstock

 

There are many eyewitness accounts by mariners of gigantic waves – almost vertical walls of water towering over ocean-going ships – that appear from nowhere and do great damage, sometimes destroying large vessels completely.

Oceanographers, who have had no way of explaining these “rogue waves”, have in the past been dismissive of such reports. But now these enormous mountains of water have been observed and measured, yielding unambiguous instrumental records. In 1985 the Fastnet Lighthouse off Ireland’s south coast was struck by a wave reported to be 48m, about the height of a 14-storey building.

The first scientifically verified rogue wave was recorded at the Draupner oil platform in the North Sea on New Year’s Day, 1995. It was about 26m high.

And in January 2014, a rogue wave higher than 29m was measured off Killard Point in Co Clare in water 40m deep.

Oceanographers describe the sea state with a statistical measure called the significant wave height. This is the average height of the one-third highest waves. A rogue wave is one that is more than double the significant wave height.

Rogue waves are sometimes called freak waves but this is misleading: although they are rare and extreme, rogue waves are part of the normal behaviour of the oceans.

Mathematicians and engineers have studied wave motion for centuries using linear models. With such models two waves can reinforce each other, producing a wave with amplitude double that of the individual components. Wave focusing can occur, but eventually the focused waves become nonlinear. Linear models cannot simulate rogue waves realistically.

In nonlinear models, wave components do not simply add up: they interact with each other and can trigger instabilities that produce extreme – if transient – peaks in wave height. The resulting rogue waves can appear suddenly and disappear again just as suddenly. When waves interact in a nonlinear fashion, some parts of the wave train can grow at the expense of others, focusing the energy in a sharp peak that is far higher than surrounding crests.

One popular equation for modelling rogue waves is the nonlinear Schrödinger equation, an elaborate analogue of the equation underlying quantum mechanics.

With nonlinear models, oceanographers can simulate the behaviour of the ocean realistically and predict the risk of heavy seas. This allows mariners to avoid dangerous areas when planning voyages. Such route planning can result in savings of thousands of euro per day in fuel consumption for a single vessel.

Rogue waves appear to have more than a single cause, depending on the initial sea state, wind speed and direction, water depth, continental shelving and other factors. Their precise origin remains a mystery and they are a subject of research.

Following the Killard wave, a research project, led by Prof Frédéric Dias of UCD, took place in early 2015 to measure extreme waves off the west coast of Ireland. A large database was assembled and several extreme waves were detected. Analysis of this data suggests that the standard explanation of rogue waves in terms of what is called modulational instability is probably invalid.

Our understanding of ocean waves continues to grow through fundamental research into the processes governing the ocean surface. As our knowledge improves, so will the accuracy of wave predictions, resulting in money and lives being saved.

The Irish Times Logo
Commenting on The Irish Times has changed. To comment you must now be an Irish Times subscriber.
SUBSCRIBE
GO BACK
Error Image
The account details entered are not currently associated with an Irish Times subscription. Please subscribe to sign in to comment.
Comment Sign In

Forgot password?
The Irish Times Logo
Thank you
You should receive instructions for resetting your password. When you have reset your password, you can Sign In.
The Irish Times Logo
Please choose a screen name. This name will appear beside any comments you post. Your screen name should follow the standards set out in our community standards.
Screen Name Selection

Hello

Please choose a screen name. This name will appear beside any comments you post. Your screen name should follow the standards set out in our community standards.

The Irish Times Logo
Commenting on The Irish Times has changed. To comment you must now be an Irish Times subscriber.
SUBSCRIBE
Forgot Password
Please enter your email address so we can send you a link to reset your password.

Sign In

Your Comments
We reserve the right to remove any content at any time from this Community, including without limitation if it violates the Community Standards. We ask that you report content that you in good faith believe violates the above rules by clicking the Flag link next to the offending comment or by filling out this form. New comments are only accepted for 3 days from the date of publication.