06/12/2019

Researchers at IMPA study the formation of a 'veil' in waves.

Os pesquisadores do IMPA Alexei Mailybaev e André Nachbin

Whether it's their imposing presence or the tranquility they convey, the movement of waves breaking on the sea fascinates everyone. Observing the ebb and flow of the water and the different shapes it takes is, for many, a simple moment of pleasure. Under the keen eye of mathematicians, this everyday mechanism of nature even becomes a subject of scientific study.

Fluid dynamics experts Alexei Mailybaev and André Nachbin from IMPA (Institute for Pure and Applied Mathematics) focused on a very peculiar aspect: the formation of a kind of "veil" that appears on the crest of a wave seconds before it breaks. Their article was featured on the cover of the Journal of Fluid Mechanics , a leading journal in the field of fluids, in March of this year.

In the publication “Explosive ripple instability due to incipient wave breaking”, the pair of mathematicians from IMPA explain that the formation of small droplets and bubbles that precedes the breaking of the wave is related to the accelerated trajectory of roughness towards the crest of the wave, resulting in a spray of particles upwards.

“When the waves begin to form, these small roughnesses on their surface accelerate towards the crest of the wave. As they approach it, they begin to decelerate, generating a compression of the roughness. Soon after, this spray upwards occurs, initiating the formation of this beautiful veil of the wave,” explains André.

It can be said that the interest in this research topic arose in the same place for both authors. Raised in the southern zone of Rio de Janeiro, André used to take his surfboard to Arpoador beach or to the now-defunct pier in Ipanema, and watch the great names of Rio's surfing scene glide down the waves during the 1970s. Meanwhile, the Russian Alexei became enchanted by the sea at Arpoador years later, and often contemplates it in a more curious way.

“I like to sit on the Arpoador rock at night to work. The strong spotlight positioned on the beach allows you to see the waves breaking in detail,” says the mathematician, who states that the literature on the phenomenon described in the article is still in its early stages.

Alexei states that this video demonstrates the compressive motion studied in the article. The image shows the mechanism that leads to the intense compression of roughness near the wave crest, precisely during the breaking process.

“This movement is behind the theoretical explanation of why the surface of the water ceases to be smooth and continuous, and breaks into thousands of droplets. It is important to emphasize that this mechanism does not explain the formation of the veil itself, but it is one of the most plausible reasons to explain it,” clarifies André.

To reach this conclusion, the researchers conducted computer simulations using a potential theory model that can even predict the moment the waves break. The compression mechanism at the crest generates a strong vertical jet, giving way to a beautiful veil of light.

"The interesting part is that this phenomenon can be seen on the beaches of Rio de Janeiro, but few people notice that it's a process that begins before the wave even turns," concludes Alexei.

To read the full article, click here .

Images of the formation of this phenomenon can be found on YouTube .

Check out the cover of the March issue of the Journal of Fluid Mechanics: