Turbulent flow snapshots

But what are these exact coherent structures? Visually, in turbulence, they may show up as fleeting moments when the patterns stop changing. And it can look like the flow is temporarily slowing down.

To the untrained eye, an ECS doesn’t look much different from the rest of the swirls and curls, but one can learn to spot them. “That’s exactly how we go about finding them,” Schatz said. “We watch the turbulence, continually taking snapshots. The flow is moving around, moving around. We look for the instant when it slows down the most, and we pick out a snapshot.”

“We feed that into the mathematical model,” Schatz said, “and it indicates that we’re close, and shows what the math looks like at that point.” That math solution describes a point in the turbulent flow that can be worked with to compute a prediction of what the turbulence will do next.

To understand what an exact coherent structure is dynamically, we need to step back from what turbulence looks like visually with bunches of curls and swirls. Instead, let’s look at a turbulent flow as a single physical entity by translating it into a crude metaphor, a swinging pendulum -- with some marked oddities.



Pendulum on its head

This is going to get a bit abstract: First, invert the pendulum.

Instead of picturing the bottom point of a normal pendulum’s swing, the equilibrium, as a stable point in a stable swing, now, with the upside-down pendulum, the equilibrium is the top-most point. And it’s unstable. Also, it doesn’t swing in just two directions but in all directions.

A turbulent flow’s reliable patterns reflect dynamics that are back-and-forth-to-and-fro but in all kinds of variations.

As the metaphorical pendulum swings up toward its peak, it comes to a near but never complete stop. Instead it flops over to some other side. That near-halt point is analogous to an exact coherent structure, but there are a few more kinks in the metaphor.

“If we change initial dynamics ever so slightly, an inverted pendulum can swing past its unstable equilibrium at the peak, or it can stop and then start moving in the opposite direction. In the same way, the turbulent flow can evolve in various different ways after passing by an ECS,” Grigoriev said.

Multiple exact coherent structures with varying qualities turn up in a turbulent flow.