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Freaks of the Sea

Image of freak wave

In 1978 the German cargo vessel MS München was struck by a freak wave 24–30 metres high. Image from Horizon – Freak Wave courtesy of BBC Worldwide. © BBC/Monkey Experiment

By Murray Rudman

Once the stuff of maritime legend, rogue waves up to 30 metres high have been detected by satellites, posing a significant threat to shipping and oil rigs. Now computational scientists are smashing virtual rogue waves into virtual oil and gas platforms to help design stronger, safer structures.

Rogue waves were once thought to be the folklore of mariners who had spent too much time at sea. Giant waves rising out of the blue in the open ocean, towering more than 20 metres in height, terrified sailors and damaged vessels.

Satellite and direct observations have now revealed that these freak waves really exist and pose a risk to ocean structures like oil rigs, as well as the workers on them. Fortunately, they are a risk that can be managed.

Freak waves, rogue waves or extreme waves, as they are variously called, are unpredictable, potentially deadly walls of water rising many times higher than neighbouring waves. To oceanographers, they are waves whose height is more than twice the significant wave height (SWH), which is defined as the mean of the largest one-third of waves in a given sea state. They are often preceded by a deep trough, which makes them appear even larger, and they may occur singly or in groups.

Unlike tsunamis, rogue waves are not caused by undersea earthquakes or landslides. What they are caused by is still largely a puzzle. Possible causes include currents, the shape of the sea bed, wind, storms and non-linear effects or interactions among these.

While rogue waves have been observed in storms like Hurricane Katrina, they have also been recorded in fine weather. Further research is needed to determine their causes.

From Folklore to Fact
Anecdotes about rogue waves include newspaper reports dating from the 1920s. The Titanic might not have survived an iceberg, but its sister ship Olympic survived several rogue waves during her 24-year service across the Atlantic. In 1925 the New York Times reported in an article entitled “Wave 72 ft high hit giant Olympic”:

Captain W. Marshall said the wave was most peculiar. The sea was not unusually rough when the wave suddenly lifted up under the Olympic and engulfed the bridge [which stood 60 ft above water level]. It played havoc with a ventilator, broke a “clear view” screen and bent the metal pedestal of a compass.

One of the best-known reports occurred in 1978 when the 37,000 tonne German cargo vessel MS München radioed a distress call from the mid-Atlantic. Suddenly faced with a wall of water 24–30 metres high, the München plunged into the trough of the huge wave. As the wave collapsed it broke across her bow, tearing the starboard lifeboat out of its pins, smashing into the bridge, breaking the windows and flooding the ship. When rescuers arrived they found only a few twisted bits of wreckage. No survivors were ever found.

Then, on New Year’s Day in 1995, a giant wave hit the Draupner oil platform in the North Sea. The rig swayed and suffered minor damage while its on-board measuring equipment recorded a wave 25.6 metres high from peak to trough. It was the first time that a rogue wave had been measured – the first incontrovertible evidence that rogue waves are real. Even now they are sometimes called “Draupner waves” after the platform that first recorded them.

Despite these and other encounters, rogue waves have been generally considered such rare events that they were not worth worrying about. Scientists had previously believed that large freak waves only occurred once every 100,000 years. As a result, ships and oil platforms are usually designed to withstand waves no higher than 15 metres.

But in 2001 European Space Agency satellites monitoring the world’s oceans picked up more than 10 giant waves over 25 metres high in a period of just 3 weeks. Not only were rogue waves real, they were more common than previously thought.

Managing the risks posed by rogue waves becomes more important once we realise that they aren’t so freakish after all. The more we can understand about them, and the way they interact with man-made structures, the better we can mitigate the risks by designing structures that can withstand them.

One approach to designing resilient structures is to use mathematical models of rogue waves that can be run on high-powered computers. The outputs of these models are then used to analyse the forces generated on the structures by the impacts of waves.

Computer Modelling
Computational fluid dynamics (CFD) is an area of mathematical modelling developed and used at CSIRO and many other research organisations around the world. Our team at CSIRO Mathematics, Informatics and Statistics has developed a range of algorithms for studying the flow of gases and liquids and the interaction between these and solid structures. We have nearly 20 people working on fluid-modelling projects ranging from dam breaks, floods and coastal inundation to writing software for animators to create realistic-looking fluid motion in movies, and even modelling high pressure die casting for car parts. We are also starting to explore biological applications, such as modelling blood flow in human arteries for medical research.

Our interest in rogue waves came from a need to predict their impacts on offshore structures for the safe design of floating oil and gas platforms. We wanted to compare different mooring designs and assess the usefulness of CFD modelling as a design and testing tool for these offshore platforms. So, in our offices in suburban Melbourne, we’ve been recreating giant rogue waves more than 20 metres high and smashing them into virtual oil and gas production platforms.

Although these kinds of experiments can be done in a wave-testing tank, such tests are expensive and the modifications required to change the platform and mooring designs can be very time-consuming. CFD allows them to be done more cheaply, more quickly and more thoroughly with no limit on the virtual sensors that can be incorporated in the CFD model.

Doing this type of modelling early in the design process helps to determine which designs are good enough to proceed to the wave tank testing phase, quickly eliminating the ones that are unlikely to make the grade. This approach helps to streamline the design process.

Simulating the Power of Nature
Waves are very powerful. All of us who have been knocked over by a wave at the beach or been dumped off a surfboard or bodyboard know that moving water can exert huge forces on objects they encounter.

Waves are also extremely difficult to predict, especially in the open ocean and when they begin to break. As a surfer, many times I’ve been dumped by a wave that I thought I could have ridden into shore.

Further, the movement of a wave and a large, heavy floating ship or oil platform influence each other in complex ways. Modelling these effects accurately combines centuries-old mathematical concepts and equations and sophisticated computational software.

The CFD technique we use is called smoothed particle hydrodynamics (SPH), which was developed many years ago by my PhD supervisor, Prof Joe Monaghan from Monash University in Melbourne. Joe developed the method for astrophysical applications such as modelling star formation and galaxies colliding.

Over the past several decades CSIRO scientists have extended the method so that we can apply it to a whole range of environmental and industrial applications. In several of these areas we’re leading the world. Benchmarking against other CFD methods shows us that for some types of problems, especially flows with a free surface, SPH is perhaps the best technique.

SPH models fluid flow by tracking millions of virtual fluid “particles” that move through a region of interest. The number of particles modelled in SPH is in the tens of millions, and the movement of each of them is considered separately. This requires considerable computer power.

The equations that describe the motion of fluids can be traced back to the 1700s. They are commonly known as the Navier–Stokes equations, and were first proposed by the Swiss mathematician Euler.

Solving these equations for each particle is an essential part of the SPH model, and ensures that the virtual fluid particles behave realistically.

In Silico Experiments
Using the SPH technique on a computer, we create a realistic rogue wave by applying a force on part of the model ocean and then aiming the resulting wave in the direction of the platform. When we run these experiments we’re interested in the effect of changing simulation parameters such as the wave impact angle, the wave height and the mooring system used, including the number of cables, the angle they make with the sea floor and properties such as cable elasticity and strength.

In one series of experiments we compared simulations of wave impacts on a 32,000 tonne semi-submersible floating platform with two different mooring systems. This type of platform has about three-quarters of its height submerged below the ocean surface, and is tethered to the ocean floor by a number of cables and/or chains.

The mooring systems we tested were a tension leg platform (TLP), where the cables are perpendicular to the sea floor, and a taut spread mooring (TSM) system, where the cables make an angle of 45° with the sea floor. Both of these are common in the oil and gas industry.

Which system better withstands the impact of a rogue wave? With a computer model we can find out quickly and cheaply.

The SPH software predicts the movement of the platform in all possible directions. The key variables for this study are

• the “surge”, which is the platform motion in the direction of the wave;

• the “heave”, which is its motion in the vertical direction; and

• the “pitch”, which measures the angle the platform deck makes with the horizontal.

If the platform surges too much as a result of wave impact, it can break drill strings and “umbilicals” that connect the platform to the oil or gas well, leading to an environmental catastrophe. If the platform heaves too much the deck can become submerged below the surface, a frightening and potentially dangerous situation for personnel on board. Finally, if the platform pitches too much, any loose items, including crew, can fall off the deck.

We found that the TLP system undergoes larger surge but smaller heave motions than the TSM system.

The results also predict the loads on the platform structure as well as the tensions in the mooring cables. In our simulations we can break the virtual mooring lines and continue the simulation. Is the platform still safe? Will it capsize? These are just two of the questions we aim to answer.

The Future
A future avenue of research that has direct relevance to Australia’s oil and gas industry involves modelling a type of facility called a Floating Production Storage and Offloading system (FPSO). These are enormous barge-like structures that accept gas from a sub-sea well through a large “umbilical” and contain all the necessary processing equipment on board to produce liquified natural gas (LNG). The LNG is also stored on the FPSO in large cryogenic tanks, and is offloaded periodically to LNG tankers that transport their cargo for onshore distribution.

FPSOs are currently being designed for use off Australia’s North-West Shelf, where they will need to stay put during cyclones. The industry needs to know how to design these FPSOs to withstand sea states generated by cyclones that will include large and rogue waves. This is important to safeguard lives and the equipment on the FPSO, and also to provide confidence to environmental and safety regulators that this mode of operation is safe. We are currently talking to petroleum and exploration companies to gauge their interest in developing the application of the SPH technique further in areas like this in their industry.

Rogue waves are fascinating and frightening, but the risks they pose can be managed with good understanding and informed design. Our research demonstrates that SPH is a useful tool for oil platform and ship designers who want to test the impact of different loads and design safer structures more efficiently.

Dr Murray Rudman is Program Leader of Computational and Mathematical Modelling at CSIRO Mathematics, Informatics and Statistics in Melbourne.