understanding turbulence

=explanation =physics



Some years ago, I was watching a stream, and there was an area where the flow went from laminar to turbulent.



Imagine a marble rolling down a slope. It rolls because there's friction where it touches the surface. This is easy enough to understand.


Now imagine laminar flow of water down a slope. Let's introduce a small "rolling" rotation in the water (a "vortex") and imagine what happens to it. The vortex is strengthened by friction with the surface, and weakened by viscosity.


The vortex is strengthened by: diameter * ((top speed - bottom speed) - rotation speed).

It's weakened by: diameter * viscosity * rotation speed.

The difference determines its growth rate.


When 2 vortices touch, this creates another vortex between them.


When the rotation speed becomes > (flow speed / 2), the shear between 2 vortices is greater than the shear of the main flow. That means shear between the new smaller vortices is greater than shear between the parent vortices, so the rotation becomes more violent as scale goes down, until the point where the vortices are comparable in size to the boundary layer.


You can see this in a stream when there are big ripples that suddenly become frothing whitewater.



With airfoils, you generally don't get turbulent flow when pressure is decreasing, and you usually do when pressure is increasing.


Consider what happens to a vortex when flow velocity is decreasing and pressure is increasing. The bottom is moving slower than the flow, so it's slowed down more than the rest of the flow when pressure increases. The top of the vortex is moving faster, so it slows down less than the rest of the flow when pressure increases. The net effect is an amplification of the vortex.


The opposite happens when flow velocity is increasing and pressure is decreasing, and the vortex is weakened.



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