We are still a long way from understanding turbulence and fluid dynamics but getting closer.*
From Quanta Magazine, July 18:
By treating Earth as a topological insulator — a state of quantum matter — physicists found a powerful explanation for the movements of the planet’s air and seas.
While much of our planet’s air and seas are stirred at a tempest’s whim, some features are far more regular. At the equator, thousand-kilometer-long waves persist amid the chaos.
In both the ocean and the atmosphere, these gargantuan waves, called Kelvin waves, always travel eastward. And they fuel oscillating weather patterns such as El Niño, a periodic warming of ocean temperatures that returns every few years.
Geophysicists have leaned on a mathematical explanation for equatorial Kelvin waves since the 1960s, but for some, that explanation wasn’t entirely satisfying. These scientists wanted a more intuitive, physical explanation for the waves’ existence; they wanted to understand the phenomenon in terms of basic principles and to answer questions like: What’s so special about the equator that permits a Kelvin wave to circulate there? And “why the heck does it always travel east?” said Joseph Biello, an applied mathematician at the University of California, Davis.
In 2017, a trio of physicists applied a different type of thinking to the problem. They began by imagining our planet as a quantum system, and they ended up making an unlikely connection between meteorology and quantum physics. As it turns out, Earth’s rotation deflects the flow of fluids in a way that’s analogous to how magnetic fields twist the paths of electrons moving through quantum materials called topological insulators. If you imagine the planet as a giant topological insulator, they said, you can explain the origin of the equatorial Kelvin waves.
But even though the theory worked, it was still only theoretical. No one had directly observationally verified it. Now, in a new preprint, a team of scientists describes the direct measurement of twisting atmospheric waves — the exact kind of evidence needed to bolster the topological theory. The work has already helped scientists to use the language of topology to describe other systems, and it could lead to new insights about waves and weather patterns on Earth.
“This is a direct confirmation of these topological ideas, gleaned from actual observations,” said Brad Marston, a physicist at Brown University and an author of the new paper. “We’re actually living inside of a topological insulator.”
Geoffrey Vallis, an applied mathematician at the University of Exeter in the U.K. who was not involved in the work, said the new result is a significant advance that will provide a “foundational understanding” of Earth’s fluid systems.
The Shape of Water
There are two ways to begin this story. The first is all about water, and it starts with William Thomson, also known as Lord Kelvin. In 1879, he noticed that the tides in the English Channel were stronger along the French coastline than on the English side. Thomson realized that this observation could be explained by the Earth’s rotation. As the planet spins, it generates a force, called the Coriolis force, that causes fluids in each hemisphere to swirl in different directions: clockwise in the north, counterclockwise in the south. This phenomenon pushes the water in the English Channel up against the French shoreline, forcing waves to flow along its coast. Now known as coastal Kelvin waves, these waves have since been observed all over the world, flowing clockwise around landmasses (with the coastline on the right side of the wave) in the northern hemisphere and counterclockwise in the southern hemisphere....
This is one of those fields of study that are so mind-bogglingly complex that, short of having a supercomputer close to hand, we can only approximate as to the details. See also weather, markets, and any other complex/chaotic system you can think of.
So anyone who can get a handle on what is actually going on with this stuff gives a whole 'nother meaning to the concept of smart....
And more recently:
June 13, 2023
Figure This Out And Make A Million Bucks: Now With Penguins
First up, the penguins, from Chalkdust, (A Magazine For The Mathematically Curious)....
Follow-up To "Figure This Out And Make A Million Bucks..."
On a much smaller scale, understanding turbulence can be worth hundreds of millions to billions of dollars when siting turbines on a wind farm.....
