Of winds and waves
The physics of breaking waves is even
more complicated than that of wave
formation by wind.
Image: iStockphoto

As Category 4 Tropical Cyclone Olivia tracked across Australia’s North West Shelf in April 1996, a wave-measuring buoy recorded a 22-metre monster passing Woodside Energy’s North Rankin A gas platform.

It is a long way from the North West Shelf to the shallow expanse of Lake George, north of Canberra, and windspeeds and wave heights are much more modest. Yet it is here that Swinburne University of Technology physicist Associate Professor Alex Babanin and his colleagues are investigating the powerful but elusive forces that make and break waves in the open ocean.

Dr Babanin and Swinburne colleague Professor Ian Young are collaborating on the research with physicist Professor Mark Donelan of the Rosenstiel School of Marine and Atmospheric Science at the University of Miami, climate modeller Dr Andrey Ganopolski of the Potsdam Institute for Climate Impact Research (PIK) and metocean engineer Jason McConochie of Woodside.

Funded by an Australian Research Council (ARC) Linkage Grant, the wave project is developing a mathematical model of the forces involved in transferring energy from the atmosphere to the ocean – one that should illuminate how extreme winds spawn waves such as Olivia’s behemoth progeny.

Along with mermaids and sea monsters, giant waves had been thought to exist only in the imaginations of mariners who had been too long at sea.

Then, on New Year’s Day 1995, a video camera and a laser recorded a wave 26 metres from trough to crest passing the Draupner oil platform in the North Sea. The Draupner wave confronted physicists, meteorologists, oceanographers and marine engineers with proof of the existence of giant waves potentially capable of sinking ships and destroying large marine structures.

Satellite-borne microwave altimeters have since confirmed that severe storms in the open ocean often spawn ‘rogue’ waves exceeding 20 metres.

In shallow coastal waters interactions with the seabed cause waves to slow, mound up and break. But Dr Babanin says that about one in 50 wind-generated waves breaks spontaneously in deep oceanic waters. The physics of this phenomenon are as elusive as those that generate rogue waves.

“Waves are generated by turbulent winds – no wind, no turbulence, no waves,” he says. “But even with an effectively limitless wave fetch (the length of water over which a given wind has blown) and wind forcing of the Southern Ocean, waves don’t grow in an unlimited manner – wave breaking limits their growth, and dissipates their energy.

“Understanding energy dissipation by ‘whitecapping’ is as important as understanding the mechanisms that generate waves.”

Dr Babanin says strong, non-linear mechanisms are involved. Over very long fetches of open ocean, a wind-driven wave will progressively accumulate energy and grow in height. Then, for no obvious reason, it will break and collapse, dissipating most of its energy in a few seconds.

“The physics of breaking waves are even more complex than the physics of wave formation by wind. All sorts of non-linear interactions are involved, from very weak to very strong. We believe the same sort of interactions can also generate freak waves up to 30 metres high.”

To a great extent, wind-generated waves mediate interactions between the atmosphere and the oceans, which have a major influence on climate.

Dr Babanin says climate modellers need a more sophisticated simulation of the processes that transfer energy and gases, such as carbon dioxide, from the atmosphere to the upper, mixed layer of the ocean; so knowledge of the physics of surface waves is very important. The research will also find application in weather forecasting, particularly in predicting extreme conditions at sea.

Woodside and other energy companies will apply the findings to ensure their offshore oil and gas platforms can survive the largest waves that nature can throw at them.

Woodside’s Jason McConochie says platforms in Australian waters, like those in the North Sea, are already sufficiently robust for essential personnel to remain on-station through the most powerful storms, as they did on the North Rankin A platform during Cyclone Olivia in 1996. The platform forms part of the North West Shelf Venture, which Woodside operates on behalf of six joint venture participants.

However, Mr McConochie, Dr Babanin and their colleagues are preparing a major experiment, funded by the ARC Linkage Grant, to measure real-world wave heights and sea currents, to determine the impacts on the offshore gas platforms during a full-blown tropical cyclone.

Some of the instruments are now being installed, in time to take measurements during the next tropical cyclone season. The data will help engineers estimate the return intervals of cyclone waves for input into the structural design of offshore platforms.

“Once we have data on wind, wave and current fields from each cyclone, we can estimate the maximum winds, wave heights and currents that are likely to occur during 100 and 1000-year cyclones,” Mr McConochie says.

Professor Donelan says cyclones are ultimately powered by heat stored in warm upper layers of the ocean. Cyclonic winds create turbulent mixing and cooling of the warm layers – a stationary cyclone would soon run out of energy and die.

At Lake George, Dr Babanin, Professor Young and Profesor Donelan have conducted experiments to measure the air/sea interaction, wave generation and dissipation.

At his laboratory in Miami, Professor Donelan has used lasers and wave tanks to measure variations in the height of passing sets of waves as individual waves variously break and subside, or constructively interfere with each other, forming larger waves.

The Lake George and wave-tank experiments have determined how waves dissipate energy by breaking, after reaching a critical height and steepness.

By establishing a limit for maximum wave height at the breaking onset, Dr Babanin, Professor Young and Professor Donelan have been able to derive a wave-dissipation function as part of the model.

“There’s a simple relation: if steepness is below a certain value, waves do not break, so there is little energy dissipation,” Dr Babanin says. “But as waves accumulate energy and grow larger and steeper, there’s a threshold steepness value at which they begin to break.

“As the dominant waves break, they cause smaller waves to break in turn, so what happens is the large scale strongly influences what happens at the smaller scale.”

Dr Babanin spent six months in Potsdam this year, working with Dr Ganopolski to integrate and test the wave model as a component of PIK’s global climate model.

The project began with tests to confirm that the model, which operates at a grid resolution of 100 square kilometres, was responsive to alterations in wind and wave properties.

Tests confirmed the model was sensitive to changes in wind fields and wave activity at this scale – increased wind speeds raised larger waves, creating greater ‘drag’ between the atmosphere and the sea surface – a first for a global climate model.

Editor's Note: A story provided by Swinburne Magazine.  This article is under copyright; permission must be sought from Swinburne University of Technology to reproduce it.