Motion System Design

Totally turbulence

Fluid dynamics comprise one wild frontier in physics that has not yet been fully tamed. Where Newton's laws neatly describe macroscopic behavior of discrete physical bodies, few such laws have yet been defined for the behavior of that special phase of matter called liquid.

One situation that arises in fluids — that of turbulence, the chaotic roiling of a fluid — is least understood of all. For this reason, physicists and engineers alike rely heavily on emperical equations and “fudge factors” to approximate turbulent situations in their models.

Andrey Kolmogorov: Universal turbulence properties

In 1941, 38-year-old Russian mathemetician Andrey Kolmogorov published a paper in which he proved that no matter the system size and initial specifics, all turbulent situations exhibit certain common characteristics. For example, turbulent fluid dissipates a finite average energy per unit mass.

Wheels of whirls

Much like a gear train, the circulating currents in turbulent fluid spur smaller wheels of rolling fluid. This tendency was first defined by Englishman Lewis Fry Richardson in his 1922 book, Weather Prediction by Numerical Process and put to rhyme:

Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity.

Continuing his exploration of graduating series in nature, Richardson later pioneered studies in fractals.

Laminar flow

The opposite of turbulence is steady, predictable fluid motion called laminar flow.

Here, steady layers or streams of fluid follow largely parallel paths that stay smooth.

As fluid in real situations is always bounded by or interacting with solid structures, much of what defines laminar flow has to do with how fluid behaves near these objects. Fluid atoms (or molecules) closest to structures move with the latter: For example, the particles nearest to the inner wall of a fixed pipe do not move at all, while subsequent layers of fluid flow increasingly faster, with those at the pipe center going fasest. Here, the fluid's momentum is proportional to flow speed.

Stoichiometric definition

Turbulent flow is characterized by three features.

1. Pressure and velocity both waver. In any given volume of turbulent fluid, these fluctuate rapidly.

2. The fluid's momentum is readily convected.

3. The even spread of momentum between atoms or molecules (what's called momentum diffusion) is low. In other words, the neat and steady increase in momentum spread from a laminar situation's boundary isn't so clean in a turbulent situation.

Da Vinci's take: In 1510, Leonardo Da Vinci studied flows in fluid and compared it to that of hair: “Observe the motion of water surfaces and how it resembles that of hair, which has two motions: One depends on hair's weight, and the other on curl direction. So too does water form whirling eddies, with one part following the chief current, and the other following incidental motion and return flow.”

Remember the Moody diagram?

The Moody diagram is the gold standard for emperical determination of whether a fluid will go turbulent. It uses the relatively common and controlled example environment of a pipe.

Werner Heisenberg (of uncertainty-principle fame) once said, “When I meet God, I am going to ask him two questions: Why relativity? Why turbulence? I believe he will have an answer for the first.” Join a discussion we'll have about recent fluid-dynamics discoveries at facebook.com/motionsystemdesign.