Time, tide and computer codes

Mathematics is fighting a fierce, long-running battle to protect our lives, homes and economies from the rising sea. Computational wave dynamics – the use of computer codes to model the behaviour of sea waves and their interaction with structures – informs engineering that can defend coastal communities and vital resources against destruction wreaked by floods and waves.

For more than twenty years, the Centre for Mathematical Modelling and Flow Analysis (CMMFA) at Manchester Metropolitan University has been at the forefront of research that uses maths to model and predict the seemingly unpredictable. It can take years to see the impact of these models, so increased robustness and speed are of the essence.

Professor Ling Qian is one of the Manchester Met researchers working on codes that improve the speed of the calculations, and are among the first to account for the effects of wave breaking, aeration and wind.

CMMFA has developed a suite of codes, known as AMAZON, over the last twenty years. The research has been almost continuously funded by the Engineering and Physical Sciences Research Council (EPRSC).  

When run on a computer, AMAZON can model real engineering problems, including the impact of sea waves on structures. With sea levels rising and an increasing need for humanity to look to solve major engineering challenges like offshore wind farms or defences against increasingly extreme storms and floods, complex mathematics like this is an unsung hero in the battle to protect our changing world.

Ling is developing AMAZON and other open-source codes to study, among other things, what happens when waves hit structures like seawalls, coastlines or even ships.

Ling said: “The code solves a set of mathematical equations that govern fluid flow. I’m interested in using our codes to model offshore renewable energy devices, like wave energy devices and also offshore wind turbines. It’s a hot topic at the moment, especially in the UK as an island country.”

The Manchester Met codes stand out among other wave-modelling techniques for being specifically suitable for modelling breaking waves. They take into account phenomena such as aeration and cavitation (the formation of cavities by pressure changes to a liquid). This is crucial when predicting wave behaviours and effects in extreme conditions.

Manchester Met researchers have been able to develop their wave modelling in three dimensions, using multiple computers to work through complex computations in parallel.

You might think that the long computational time that has mathematicians scratching their heads would be a matter of minutes or hours. It’s actually months, or even years.

“That’s why we use parallel computing,” says Ling. “We run the code on multiple machines in order to reduce computational time. In an extreme case, it can take months if not a few years to get a solution on a single computer.”

Parallel computing drastically reduces the time it takes to get an answer, bringing engineers closer, more quickly, to designs that protect structures from extreme wave conditions.

This innovation cannot arrive soon enough. In the IPCC Special Report on the Ocean and Cryosphere in a Changing Climate (2019), scientists concluded that by 2050, extreme coastal flooding - previously something that happened around once in a century - could be happening every year.

Further analysis for the UK has shown that large swathes of Norfolk and the East Coast are at significant risk, especially when rising sea levels combine with rough seas and high tides.

Protecting communities

Engineering innovations are urgently needed to protect the communities most at risk – or at least to buy time before large-scale evacuations are inevitable. Far from being abstract, complex computations are critical to preventing structural damage, loss of resources and loss of life.

Applications of the AMAZON codes are already at work across the UK:

The Bacton Gas Terminal in Norfolk is considered the UK’s most important energy hub, but in 2013 it was close to being at the mercy of the waves. The worst storm surge for a hundred years eroded the land to such an extent that only 15 metres were left between the hub and the sea.

Bacton processes a third of the UK’s natural gas supplies and is the terminus of the UK’s only gas supply lines from continental Europe. Along with hundreds of nearby homes, this critical piece of national infrastructure was now at serious risk from the sea.

Dutch engineering firm Royal HaskoningDHV proposed a ‘sand engine’ to replenish the beach around the Bacton terminal. Beaches act as a barrier to waves. Sand engines replace sand, to add decades to the lifespan of a beach or to recreate beaches that have almost disappeared. AMAZON was used to determine the shape of the beach and where the replacement sand should be placed.

The new beach was ‘sandscaped’ along a 6km stretch of the coast. At its highest level, the new beach and dune now stands 7m above previous levels and extends as much as 250m out to sea. It is designed to protect against a 1-in-10,000 year storm.

The seaside community of Littlehaven has also benefited from AMAZON.  The town’s award-winning ‘Floodtastic Wonderwall’ was designed using AMAZON and is helping to protect the town and its businesses from frequent flooding. AMAZON was an appropriate and cost-effective way of modelling the shape of the wall needed. The result was a structure that protects livelihoods and homes and is widely considered to be easier on the eye than some other coastal defences.

renewable energy 

Ling has long been interested in using AMAZON and other open-source codes to model the impact of waves on offshore renewable energy devices, like wave energy devices and offshore wind farms. His current research models the performance of wind turbines once they’re placed in deeper water, requiring floating support structures.

Fixed support structures for wind turbines in deep water are usually too expensive to be sustainable. Ling’s research looks at extreme loading on floating offshore wind turbines under storm conditions to inform the design of the more stable and cost-effective floating structures.

While change led by computational wave dynamics can take years, it’s clear that improvements like those made by AMAZON could make a very real difference to our sustainable future.

As the world looks more and more to renewable energy sources, the knowledge gained through Ling’s research is timely and urgent. Ling is keen to emphasise, though, that the research is no quick fix to the world’s energy needs:

“The impact of academic research takes time. It’s my sincere hope that in five or ten years’ time our research will generate even greater real impact in the design and deployment of the next generation of floating offshore wind turbines.”

While change led by computational wave dynamics can take years, it’s clear that improvements like those made by AMAZON could make a very real difference to our sustainable future.