When the wave expands to a critical height, it will break up, and then fall into a shower of water droplets and bubbles at the wave crest. These waves can be as big as a surfer's breaking point and as small as gentle ripples rolling to the shore. For decades, the dynamics of how and when waves break have been too complex for scientists to predict.
Data map
Now, engineers from the Massachusetts Institute of technology have found a new way to simulate how waves break. Using data from machine learning and wave tank testing, the researchers adjusted the equations previously used to predict wave behavior. It is reported that engineers often use this equation to help them design robust offshore platforms and structures. But until now, these equations can not capture the complexity of breaking waves.
The researchers found that the modified model could more accurately predict how and when waves would break. For example, compared with the traditional wave equation, the model can more accurately evaluate the wave steepness shortly before breaking, and the energy and frequency after breaking.
Their work, recently published in nature communications, will help scientists understand how breaking waves affect the water around them. An accurate understanding of how these waves interact can help in the design of offshore structures. In addition, it can improve the prediction of the interaction between the ocean and the atmosphere. With better estimates of how waves break, scientists can predict such issues as how much carbon dioxide and other atmospheric gases the ocean can absorb.
Themis sapsis, the study's author, said: "this may sound like a detail, but if you multiply its impact by the area of the entire ocean, breaking waves begin to become fundamental to climate prediction." Sapsis is an associate professor of mechanical and ocean engineering and a member of the MIT Institute of data, systems and society.
Learning tank
In order to predict the dynamics of breaking waves, scientists usually adopt one of the following two methods - they either try to accurately simulate waves on the scale of individual water and air molecules, or try to describe the characteristics of waves through experiments with actual measurements. The first method is expensive and difficult to simulate even in a small range; The second method requires a lot of time to conduct enough experiments to produce statistically significant results.
MIT's team borrowed some fragments from these two methods, and then developed a more effective and accurate model using machine learning. The researchers began with a set of equations known as standard descriptions of wave behavior. Their goal is to improve the model by "training" the model on the breaking wave data in actual experiments.
The researchers obtained the breaking wave data by conducting experiments in a 40 meter long water tank. One end of the tank was fitted with an oar, which the team used to start each wave. The team set the paddle to produce a breaking wave in the middle of the tank, and then measured the height of the water along the length of the tank.
"These experiments take a lot of time. Between each experiment, you have to wait for the water to completely calm down before starting the next experiment, or they will affect each other," eeltink said.
Safe harbor
It is understood that the research team conducted about 250 experiments in total, and they used the data to train a machine learning algorithm called neural network. Specifically, the algorithm is trained to compare the real wave in the experiment with the predicted wave in the simple model. According to any difference between the two, the algorithm adjusts the model to adapt to the reality.
After training the experimental data, the research team introduced the model into the new data. In this case, measurements from two independent experiments, each running in a wave trough of different sizes. In these tests, the researchers found that the updated model made more accurate predictions than the simple, untrained model.
In addition, the new model also captures a basic property of the breaking wave, that is, "down shift", that is, the frequency of the wave is shifted to a lower value. The speed of a wave depends on its frequency. For waves, low-frequency waves move faster than high-frequency waves. Therefore, after moving down, the wave will move faster. The new model predicts changes in frequency before and after each breaking wave, which may be particularly useful in preparing coastal storms.
The research team's updated wave model is in the form of open source code, which means that others may use it. In addition, the code can also be used for simulation testing of offshore platforms and coastal structures.
Sapsis said, "the primary purpose of this model is to predict what waves will do. If you do not correctly simulate breaking waves, it will have a huge impact on the behavior of the structure. With this, you can simulate waves to help better and more effective design of the structure without a huge safety factor."