SIAM News Blog

Modeling Ocean Waves Improves the Safety of Search and Rescue Ships

By Lina Sorg

The study of ocean waves finds many applications in the fields of naval architecture and coastal/ocean engineering. Understanding the dynamics of their generation and dispersion is also important for offshore vessels, which must successfully navigate these nonlinear, variable waves. For instance, changing weather and ocean conditions can trigger funneling effects, which rapidly transform manageable waves into swells that are tens of meters high and can easily capsize ships.

The velocity of fast-moving ships, like those employed in search and rescue missions, make them especially vulnerable to abnormally high “freak waves.” These ships can reach speeds of up to 30 knots (nearly 35 miles per hour), and are vital to many offshore procedures. In addition to disaster response, they are frequently used in anti-drug and anti-piracy expeditions, to deliver supplies to offshore oil and gas platforms, and to transport workers who maintain wind farms. Around 100 fast ships are lost or damaged in rough water each year. In 2013, these accidents resulted in approximately 2,500 casualties.

With support from the Engineering and Physical Sciences Research Council, researchers at the University of Leeds (UK) have created a computer model that could facilitate the development of safer fast ships. The model, based on complex mathematics, simulates and animates interactions between waves that cause abnormally high swells. Adding the motion of ships into this model allows them to illustrate how sea waves can affect fast ships. The researchers simulate freak waves in a Hele-Shaw tank, a slim wave tank with two closely-spaced glass panels on either side. A wave pump generates constant water motion, and the tank’s narrowness generates a water flow that is nearly two-dimensional and thus easy to observe. So far, the model’s estimates of ocean waves’ effects on fast-moving vessels have been remarkably accurate.


While use of potential flow theory is often standard when studying nonlinear water waves, classical potential flow theory can be simplified for shallow water waves. Luke’s variational principle also permits the study of water wave dynamics. The researchers expand the variational principle for shallow water to develop equations that manage the model’s hydrodynamics. They add boundary conditions, the effects of surface tension, and an exponential, time-dependent term representing linear damping to make their simulations more accurate and to better understand the pressure forces that affect vessels at sea.

According to Anna Kalogirou, co-author of the study, the simulation tool also measures pressures on the ships’ surfaces and amplitudes of the surrounding waves. Read more of the researchers’ thoughts here.

Because including the motion of the rapidly-moving ships complicates the model’s equation, the team plans to refine and expand the model over the next few years. They hope that their simulations will ultimately help maritime engineers and ship designers craft fast ships that are more suitable for rapid and unexpected wave motion.

Click here to view the corresponding journal paper.


  Lina Sorg is the associate editor of SIAM News 


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