Some Turbulence Ahead

Turbulent flow from a candle

Richard Feynman in 1970 described turbulence as the most important unsolved problem of classical physics. Sir Horace Lamb (in a speech to the British Association for the Advancement of Science in 1932) said that “when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic.” Werner Heisenberg was asked what he would ask God, given the opportunity. His reply was: “When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first.”

Yet turbulence is all around us. It rattles our teeth on cross-country jet flights; we see it in smoke out of smokestacks and the wakes of boats; it makes curveballs curve and golf balls fly long distances; it creates ocean waves and makes snow drifts. We can see it in the atmosphere of Jupiter.

NASA/JPL-Caltech/SwRI/MSSS/Roman Tkachenko

And, really, we don’t understand it.

In the candle smoke photo, the smoke is smoothly flowing for a bit. That’s called “laminar flow.” But the smoke quickly shifts to a chaotic, jumbled mess. That’s turbulent flow.

Without getting in to math that’s beyond the edge of WC’s foggy arithmetic skills,¹ here are the things we know:

Turbulent flows are always highly irregular. For this reason, turbulence problems are normally treated statistically rather than deterministically.

Turbulent flow is chaotic.² With greatly improved computer storage and calculating power, the science of turbulence is beginning to deal with larger datasets instead of treating it statistically, but that hasn’t generated anything helpful yet. We’ll come back to this approach.

The readily available supply of energy in turbulent flows tends to accelerate the homogenization (mixing) of fluid mixtures. The characteristic which is responsible for the enhanced mixing and increased rates of mass, momentum and energy transports in a flow is called “diffusivity”. Turbulence promotes the averaging of energy in systems.

If you have enough information about a system, you can predict the onset of turbulence. It’s the Reynolds Number, which is defined as:

where:

• ρ is the density of the fluid (SI units: kg/m³)
• v is a characteristic velocity of the fluid with respect to the object (m/s)
• L is a characteristic linear dimension (m)
• μ is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/(m·s)).

WC will spare you the arithmetic. Flows at Reynolds numbers larger than 5000 are typically (but not necessarily) turbulent, while those at lower Reynolds numbers usually remain laminar. It’s less helpful in understanding turbulence than you’d think.

Turbulence increases heat exchange and friction: it heats the medium in which it is occurring. We can kinda/sorta measure turbulence by measuring that heat. But the math is pretty hairy and it doesn’t answer the question of “Why?”

Some very bright people, ranging from Werner Heisenberg to Andrey Kolmogorov have proposed theories but they haven’t been experimentally confirmed. Or have been disproved. even Leonardo da Vinci took a crack at it.

Leonardo da Vinci’s sketch of water exiting from a square hole into a pool; circa 1500.

But to date, there hasn’t ben a lot of progress. But there are developments. Techniques like particle image velocimetry, laser-induced fluorescence and laser Doppler anemometry allow scientists to track the behavior individual molecules in a turbulent flow. The bad news is that existing storage and processing equipment are quickly overwhelmed tracking the millisecond by millisecond motions of billions of molecules. So the datasets have to be managed statistically.

The traditional statistical approach of averaging data over time, which itself is computationally challenging enough, largely ignores the large excursions from the mean that are typically observed near sharp interfaces in turbulent flows. Physicists are trying to develop new mathematical tools that don’t bury those variances in the statistical means. So far those tools are promising but really untested. Nor have they provided any new insights.

So we’re back where we started. We really don’t understand turbulence.

Want to be famous? Develop testable theories that accurately predict and describe turbulent flow. Go ahead; WC will wait.

 

 

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1. Remember: if WC could do arithmetic, he wouldn’t have had to go to law school. ↩
2. But not all chaotic flows are turbulent. Nope, we don’t really know why that is, either. ↩