Came across a recent <a href=http://www.wired.com>Wired</a> article: Why don't we understand turbulence?.

Wonder if anyone might have something to add or comment? A wiki area is available to capture the debate.

Here's my response posted on the Wired wiki:

The article touches on the essence of chaotic systems, i.e. acute sensitivity to initial conditions or the butterfly effect. If applied to weather forecasts, it would read 'Why do five day weather forecasts suck?', making an apt article. However, to single out turbulence as a mystery is misguided. Airplanes don't fall out of the sky due to turbulence precisely because we have a deep understanding of turbulence.

A full description of fluid flow, including turbulence, is contained within the Navier-Stokes equations, dating from the mid 19th century. With the advent of computers, engineers have solved various forms of these equations within the field known as Computational Fluid Dynamics (CFD). Chaos theory and cellular automata, cited in the article, are at best bit players.

>Airplanes don't fall out of the sky due to turbulence precisely because we have a deep understanding of turbulence.

I do not recall any airplane falling out of the sky due to turbulence, with or without understanding. Airplanes have been flown before even laminar boundary-layer theory was established, and some have crashed for various reasons, but I don't remember turbulence being one of them. In other words, not understanding turblence does not prohibit us from flying airplanes. Your suggestion that airplanes would fall out of the sky if we didn't understand turbulence is simply false.

> A full description of fluid flow, including turbulence, is contained within the Navier-Stokes equations, dating from the mid 19th century.

There is a not so subtle difference between knowing and solving a system of governing equations and fully "understanding" the nonlinear phenomena it describes. You can regard CFD along with other numerical techniques as a way to obtain a particular (not general) solution to equations that we don't fully understand. If we fully understood it, we'd know the general anlytical solution and wouldn't depend on numerical methods. It is that lack of understanding and insufficiency of current nonlinear theories that forces us to apply numerical methods. In other words, the ability to obtain particular solutions does not require a full understanding of the nonlinear phenomena described by the equations, such as turbulence.

I read your response as an attempt to prove that we do understand turbulence, but so far, you have said nothing to convince me that that's the case... and I haven't even read that article that you quote.

The original article I'm commenting on implied that turbulence is responsible for airplanes suddenly losing lift, which I over dramatized to be 'airplanes falling out of the sky'. The article went on to imply that if we better understood turbulence airplanes wouldn't lose lift.

I was making the point that airplanes are not at the whim of a poorly understood phenomenon. The reality is that we understand turbulence enough to use it to enhance airplanes in terms of lift and drag, whether it's avoiding turbulence using laminar flow wings or triggering turbulence with vortex generators on wings.

Maybe I implied a total understanding where I really meant a good (deep) understanding of turbulence. However, I don't believe fully understanding a physical phenomenon comes with analytic solutions. All physical insights (excluding experiments) come from modeling (idealizing) a system and just because one model reduces to an analytic form and another model requires numerical methods doesn't make one or the other superior. Analytic solutions suffer the same fate as numerical methods when assumptions are wrong; you just get to the wrong answer sooner.

Given that we don't have 'one general analytic solution' to all turbulence, it is through examining a range of particular solutions (e.g. turbulent boundary layers, turbulent wakes, shear flows) we build up our knowledge base, which I maintain is now extensive.

Actually aeroplanes need turbulence to remain in the air. If the flow was laminar then there would be the potential for flow separation which would reduce the lift and potentially stall the plane. This is why there are small vortex generators on the leading edge of winds (by making the flow turbulent all along the wing the boundary layer more likely to stay attached).

So we agree, we don't "fully" understand turbulence. But more precisely, how well do we understand it? Sure, fully developed pipe flow is simple enough, but understanding turbulence in my mind includes the understanding of its onset, i.e. transition. Are we able to predict the transition of boundary layers on an airplane surface (wing, fuselage) and turbine blades at various Mach and Reynolds numbers? As far as I know, the only modestly useful transition models we have are heavily based on empiricism calibrated for a particular flow and application. That's not a very strong case for "understanding". It's not that we have no clue at all, but of all the aspects of fluid dynamics, turbulence is definitely among the most obscure. Every time a new theory comes up (fractals, chaos, ...) the fluid dynamics community gets all excited about finally finding the holy grail. None of it has really worked, yet, which means... there's more excitement head of us.

I believe that it has a lot to do with wave phenomena... vibrations, oscillations & bifurctions. My friend nabla_v & it's complex principal gradients provide some very interesting insights along the way.

I'm beginning to sway towards investigating quaternion structures to better understand the time-space coupling a little better.

Lots of room for investigation.

desA

Isn't this subject inherently unfathomable? I suppose that's why a few great scientists recently wished they would go to Heaven (if they make it) and ask God itself about turbulence. But it's a fun area to theorize and attempt to model on. The world has to move on still whether or not we understand things down to the tiniest bits of details.