Physicists Describe Superfluid Turbulence with Black Hole Mathematics

Superfluids are amazing substances, moving like a completely frictionless liquid. It looks as if it can propel itself without any hindrance from gravity or surface tension. Now, physicists have taken a closer look at these superfluids, coming up with a mathematic way to describe them and the turbulent flow within them.

In order to mathematically describe the physics of a superfluid's turbulence, the researchers drew comparisons to the physics governing black holes. While at first glance these black holes may not seem to behave like a fluid, the researchers employed a technique called holographic duality.

"Turbulence provides a fascinating window into the dynamics of a superfluid," said Allan Adams, an associate professor of physics at MIT, in a news release. "Imagine pouring milk into a cup of tea. As soon as the milk hits the tea, it flares out into whirls and eddies, which stretch and split into filigree. Understanding this complicated, roiling turbulent state is one of the great challenges of fluid dynamics. When it comes to superfluids, whose detailed dynamics depend on quantum mechanics, the problem of turbulence is an even tougher nut to crack."

Holographic duality, though, became the nut cracker. This particular mathematical principle can be described by envisioning a theoretical lake that's split into two layers: an overlying 2-D surface and a 3-D interior. On the lake's surface, there is no gravity--an environment that can best be described by particle theory. The underlying interior, in contrast, consists of tiny strings that vibrate, fuse and break apart to create matter and gravity--an environment that can be mathematically explained by string theory.

The researchers used this method as a "dictionary" to translate the very well-characterized physics of black holes to the physics of superfluid turbulence. Surprisingly, the scientists found that turbulent flows of a class of superfluids on a flat surface behave not like those of ordinary fluids in 2-D, but more like 3-D fluids, which morph from relatively uniform, large structures to smaller and smaller structures.

What does this mean? It's rather like the way cigarette smoke disperses in the air into smaller and smaller eddies. This particular phenomenon is known as an "energy cascade."

"For superfluids, whether such energy cascades exist is an open question," said Hong Liu, an associate professor of physics at MIT, in a news release. "People have been making all kinds of claims, but there hasn't been any smoking-gun type of evidence that such a cascade exists. In a class of superfluids, we produced very convincing evidence for the direction of this kind of flow, which would otherwise be very hard to obtain."

The findings are published in the journal Science.