Waves break as they swell to critical heights before reaching their apex and crashing into a mist of droplets and bubbles. These waves can be as big as a surfer’s tip break and as small as a gentle ripple rolling toward shore. For decades, the dynamics of how and when a wave breaks has been too complex to predict.
Now MIT engineers have found a new way to model how waves break. The team used machine learning along with data from wave tank experiments to modify equations traditionally used to predict wave behavior. Engineers typically rely on such equations to help them design resilient offshore platforms and structures. But so far the equations have failed to capture the complexity of breaking waves.
The updated model made more accurate predictions of how and when waves break, the researchers found. For example, the model estimated the steepness of a wave just before breaking, and the energy and frequency after breaking, more accurately than the conventional wave equations.
Their results, published today in the magazine nature communication, will help scientists understand how a breaking wave affects the water around it. By knowing exactly how these waves interact, the design of offshore structures can be honed. It could also improve predictions for the ocean’s interaction with the atmosphere. For example, with better estimates of how waves break, scientists can predict how much carbon dioxide and other atmospheric gases the ocean can absorb.
“Wave breaking is what brings air into the ocean,” said study author Themis Sapsis, an associate professor of mechanical and ocean engineering and an affiliate of the Institute for Data, Systems, and Society at MIT. “It may sound like a detail, but when you multiply its effect over the entire ocean area, wave breaking becomes fundamental to climate prediction.”
The study’s co-authors are lead author and MIT postdoc Debbie Eeltink, Hubert Branger and Christopher Luneau of the University of Aix-Marseille, Amin Chabchoub of the University of Kyoto, Jerome Kasparian of the University of Geneva and TS van den Bremer of Delft University of Technology.
To predict the dynamics of a breaking wave, scientists usually take one of two approaches: they either try to accurately simulate the wave at the scale of individual molecules of water and air, or they conduct experiments to characterize waves with actual measurements. . The first approach is computationally expensive and difficult to simulate, even over a small area; the second requires an enormous amount of time to run enough experiments to yield statistically significant results.
The MIT team instead borrowed pieces from both approaches to develop a more efficient and accurate model using machine learning. The researchers started with a series of equations that are considered the standard description of wave behavior. They wanted to improve the model by “training” the model on breaking wave data from actual experiments.
“We had a simple model that doesn’t capture wave breaking, and then we had the truth, i.e. wave breaking experiments,” explains Eeltink. “Then we wanted to use machine learning to learn the difference between the two.”
The researchers obtained wave-breaking data by conducting experiments in a 40-meter-long tank. The tank was fitted with a paddle at one end that the team used to launch each wave. The team deployed the paddle to produce a breaking wave in the center of the tank. Meters along the length of the tank measured the height of the water as the waves propped up through the tank.
“It takes a lot of time to carry out these experiments,” says Eeltink. “Between each experiment, you have to wait for the water to settle completely before starting the next experiment, otherwise they will influence each other.”
In total, the team conducted about 250 experiments, using the data to train a type of machine learning algorithm known as a neural network. Specifically, the algorithm is trained to compare the real waves in experiments with the predicted waves in the simple model, and based on any differences between the two, the algorithm aligns the model with reality.
After training the algorithm on their experimental data, the team introduced the model to entirely new data — in this case, measurements from two independent experiments, each performed on separate wave tanks of different sizes. In these tests, they found that the updated model made more accurate predictions than the simple, untrained model, for example, better estimates of the steepness of a breaking wave.
The new model also captured an essential property of wave breaking known as the “downshift”, which shifts the frequency of a wave to a lower value. The speed of a wave depends on its frequency. For ocean waves, lower frequencies move faster than higher frequencies. Therefore, the wave will move faster after downshifting. The new model predicts the change in frequency, before and after each breaking wave, which may be especially relevant in preparing for coastal storms.
“If you want to predict when high waves from a swell will reach a harbor, and you want to leave the harbor before those waves arrive, then the speed at which the waves are approaching is wrong if you get the wave frequency wrong,” Eeltink says.
The team’s updated wave model takes the form of open-source code that others could potentially use, for example in climate simulations of the ocean’s ability to absorb carbon dioxide and other atmospheric gases. The code can also be incorporated into simulated testing of offshore platforms and coastal structures.
“The main purpose of this model is to predict what a wave will do,” Sapsis says. “If you don’t model wave breaking properly, it would have huge implications for the behavior of structures. This would allow you to simulate waves to design structures better, more efficiently and without huge safety factors.”
This research is supported in part by the Swiss National Science Foundation and by the US Office of Naval Research.