On a calm day, a light breeze might barely ripple the surface of a lake on Earth. But on Saturn's largest moon Titan, a similar mild wind would kick up 10-foot-tall waves.
This otherworldly behavior is one prediction from a new wave model developed by scientists at MIT. The model is the first to capture the full dynamics of waves and what it takes to whip them up under different planetary conditions.
In a study published in the Journal of Geophysical Research: Planets, the MIT team introduces the model, which they've aptly coined "PlanetWaves." They apply the model to predict how waves behave on planetary bodies that might host liquid lakes and oceans, including Titan, ancient Mars, and three planets beyond the solar system.
The model predicts that a gentle wind would be enough to stir up huge waves on Titan, where lakes are filled with light liquid hydrocarbons. In contrast, it would take hurricane-force winds to barely move the surface of a lake on the exoplanet 55-Cancri e, which is thought to be a lava world covered in hot, dense liquid rock.
"On Earth, we get accustomed to certain wave dynamics," says study author Andrew Ashton, associate scientist at the Woods Hole Oceanographic Institution (WHOI) and faculty member of the MIT-WHOI Joint Program. "But with this model, we can see how waves behave on planets with different liquids, atmospheres, and gravity, which can kind of challenge our intuition."
The team is particularly keen to understand how waves form on Titan. The large moon is the only other planetary body in the solar system other than the Earth that is known to currently host liquid lakes.
"Anywhere there's a liquid surface with wind moving over it, there's potential to make waves," says Taylor Perron, the Cecil and Ida Green Professor of Earth, Atmospheric and Planetary Sciences at MIT. "For Titan, the tantalizing thing is that we don't have any direct observation of what these lakes look like. So we don't know for sure what kind of waves might exist there. Now this model gives us an idea."
If humans were to one day to send a probe to Titan's lakes, the team's new model could inform the design of wave-resilient spacecraft.
"You would want to build something that can withstand the energy of the waves," says lead author Una Schneck, a graduate student in MIT's Department of Earth, Atmospheric and Planetary Sciences (EAPS). "So it's important to know what kind of waves these instruments would be up against."
The study's co-authors include Charlene Detelich and Alexander Hayes of Cornell University and Milan Curcic of the University of Miami.
"The first puff"
When wind blows over water, it creates waves that can be strong enough to carve out coastlines and redistribute sediment brought to the coast by rivers. Through this process, waves can be a significant force in shaping a landscape over time. Schneck and her colleagues, who study landscape evolution on Earth and other planets, wondered how waves might behave on other worlds where gravity, atmospheric conditions, and liquid compositions can be very different from what is found on Earth.
"There have been attempts in the past to predict how gravity will affect waves on other planets," Schneck says. "But they don't quantify other factors such as the composition of the liquid that is making waves. That was the big leap with this project."
She and her colleagues developed a full wave model that takes into account not just a planet's gravity, but also properties of its surface liquid, such as its density, viscosity, and surface tension, or how resistant a liquid is to rippling. The team also incorporated the effect of a planet's atmospheric pressure. With this model, they aimed to predict how a planet's liquid surface would evolve in response to winds of a given speed.
"Imagine a completely still lake," Ashton offers. "We're trying to figure out the first puff that will make those first little tiny ripples, on up to a full ocean wave."
Making waves
The team first tested their new model with wave data on Earth. They used measurements of waves that were collected by buoys across Lake Superior over 20 years. They found that the model, which took into account Earth's gravity, the composition of liquid (water), and atmospheric conditions, was able to accurately predict what windspeeds it would take to generate waves across the lake, and how high the waves grew with a given wind strength.
The researchers then applied the model to predict how waves would behave on other planetary bodies that are known to host liquid on their surface. They looked first to Titan, where NASA's Cassini mission previously captured radar images of lake formations, which scientists suspect are currently filled with liquid methane and ethane. The team used the new model to calculate the moon's wave dynamics given its gravity, atmospheric pressure, and liquid composition.
They found that on Titan, it's surprisingly easy to make waves. The relatively light liquid, combined with low gravity and atmospheric pressure, means that even a gentle wind can stir up huge waves.
"It kind of looks like tall waves moving in slow motion," Schneck says. "If you were standing on the shore of this lake, you might feel only a soft breeze but you would see these enormous waves flowing toward you, which is not what we would expect on Earth."
The researchers also considered wave activity on ancient Mars. The Red Planet hosts many impact basins that may have once been filled with water, before the planet's atmosphere dissipated and the water evaporated away. One of those basins is Jezero Crater, which is currently being explored by NASA's Perseverance rover. With the new model, the team showed that as Mars' atmosphere gradually disappeared, reducing its pressure over time, it would have required stronger winds to make the same waves.
Beyond the solar system, the researchers applied the model to three different exoplanets. The first, LHS1140b, is a "cool super-Earth," meaning that it is colder and larger than Earth. The planet hosts liquid water, though because it is so large, it has a stronger gravity. The model showed that the same wind on Earth would generate much smaller waves of water on the super-Earth, due to its difference in gravity.
The team also considered Kepler 1649b, a Venus-like planet, which has a gravity similar to Earth's, with lakes of sulfuric acid, which is about twice as dense as water. Under these conditions, the researchers found that it would take strong winds to make even a ripple on the exo-Venus, compared to on Earth.
This effect is even more pronounced for the third planet, 55-Cancri e — a lava world that has both a higher gravity than Earth and a much denser, more viscous surface liquid. Scientists suspect that the planet hosts oceans of liquefied rock. In this environment, the model predicts that hurricane-force winds on Earth, of about 80 miles per hour, would generate only small waves of a few centimeters in height on the lava world.
Aside from illuminating new ways that waves can behave on other planets, Perron hopes the model will answer longstanding questions of planetary landscape formation.
"Unlike on Earth where there is often a delta where a river meets the coast, on Titan there are very few things that look like deltas, even though there are plenty of rivers and coasts. Could waves be responsible for this?" Perron wonders. "These are the kinds of mysteries that this model will help us solve."
This work was supported, in part, by NASA and the National Science Foundation.
