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Why do boundary layers become more turbulent as they flow over a surface? This question originated from this one.

What makes the boundary become more turbulent as it flows over a surface/wing? My suspicion is that it's from the varying speeds over the boundary layer (which becomes greater over a bigger surface), but why would that cause turbulence?

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As a flow progresses, tiny perturbations happen. In some flows, these perturbations are quickly damped out as if nothing happens. This is a laminar flow. In other flows, these perturbations grow and cause more perturbations. This is a turbulent flow.

Whether turbulence happens is therefore a stability problem. Will the tiny perturbation stay the same? Will it be damped out? Will it grow out of control?

There are two reasons that turbulence increases along the length of a flow. 1) you've had more opportunities for random perturbations, so turbulence is more likely. 2) the character of the flow changes with the length of a boundary layer such that a formerly stable flow becomes an unstable flow.

The Reynolds number is the ratio of the inertial force to the viscous force on a fluid element. I.e. the ratio of the effects of the fluid element's momentum to the effects of viscosity in and on the fluid element. You can probably imagine that if the inertia greatly outweighs the viscosity that you will have a different characteristic of flow than if the viscosity greatly outweighs the inertia. The Reynolds number increases along the length of a flow -- so the fundamental character of the flow (inertial vs. viscous effects) changes along the length. The stability of the flow (whether perturbations grow or shrink) also changes along with it.

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  • $\begingroup$ Oh I see, thanks. One question: Why does the character of the flow change along the BL? What makes it change? $\endgroup$
    – Wyatt
    Jan 29 at 15:45
  • $\begingroup$ @Wyatt Please re-read my answer. The Reynolds number represents the ratio of inertial force to viscous force. That ratio changes along the BL (because it is a function of the flow length along the BL). At some Re, inertia dominates -- at a different Re, viscous dominates. The flow fundamentally has different character. It changes from stable to unstable. Think about driving on an icy road. For some speed and mass, you are stable -- but too much inertia and you'll go unstable. What if the road is only wet? What if it is dry? The ratio of the inertia to viscous is what matters. $\endgroup$ Jan 29 at 17:19
  • $\begingroup$ That makes a lot more sense. Up until now I didn't really understand how the Reynolds number worked, but you helped me understand it. Seems like a very useful tool for determining if flows will be turbulent or laminar, (or in between). Thanks $\endgroup$
    – Wyatt
    Jan 29 at 20:22
  • $\begingroup$ Also one last little question : is it possible for the boundary layer to not become more turbulent as it goes over the wing? In a more perfect situation though. $\endgroup$
    – Wyatt
    Jan 29 at 20:43
  • $\begingroup$ In an external flow, the probability of a flow to transition to turbulent will increase with flow length. If the Reynolds number is sufficiently low, transition is impossible and the flow will remain laminar. There are some boundary layer control techniques (such as boundary layer suction) that can substantially delay the transition to turbulence. Internal flows (inside pipes, between concentric cylinders, etc) can have very different character and a different world. Note that turbulence is an area that physics, math, and engineering does not yet have a complete theoretical model of. $\endgroup$ Jan 29 at 22:33
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What makes the boundary become more turbulent as it flows over a surface/wing?

There are so many people who know much more about this than I. But let's just discuss this simply regarding low mach number wings and flight, say Reynolds numbers more than a million but less than 10 million. Typically, two things contribute to turbulence: a) intrinsic factors, and b) extrinsic factors.

Let's take a look at the intrinsic factors, first. As the flow progresses over the wing from leading edge to trailing edge, the flow initially accelerates to a maximum velocity (about mid-chord, say somewhere between 30 and 60 percent of the chord length), and then decelerates to the trailing edge. We call this initial acceleration a favorable pressure gradient, and the deceleration region an adverse pressure gradient. The favorable pressure gradient promotes the growth of the laminar boundary layer. At the initiation of the deceleration phase, however, the laminar boundary layer is destabilized and forms a laminar separation bubble, which itself increases drag. The laminar boundary layer is destabilized by the loss of the favorable pressure gradient and becomes turbulent as the flow reattaches and progresses against the adverse pressure gradient. No longer is the velocity of the boundary layer zero at the surface of the airfoil, as it was with the laminar boundary layer, but the energized flow is now actively moving against the surface. As this turbulent boundary layer progresses against the adverse-pressure gradient, the turbulent layer becomes thicker and will increase skin-friction drag with the airfoil. The adverse gradient can cause the turbulent layer to separate resulting in a marked increase in pressure drag. Momentum from the aircraft is now transferred into the turbulent airstream separating from the wing. The wing has stalled. However, this is not always true. Airfoils can be designed in such a way that the shape of the airfoil controls the gradient of deceleration against which the turbulent boundary layer must progress. In fact, the shape of the airfoil profile through this region can be designed in such a way that the boundary layer becomes infinitely separating and produces no skin friction or pressure drag as the flow separates.

What are extrinsic factors? Bugs. Dust, surface imperfections, dents, rivets, rain, the propeller. Any of these items can trip the laminar boundary layer causing it to become turbulent in the favorable pressure gradient of the airfoil. This increases drag. As this flow accelerates, the turbulence generated thereby becomes fully energized and will thicken precipitously as the flow progresses through the adverse pressure gradient. Nevertheless, this process can be propitiously used to advantage. If a trip strip is placed on the surface of the airfoil in the favorable pressure gradient region just ahead of the adverse-pressure gradient where the laminar boundary layer will separate, the tripped laminar layer will become turbulent and remain attached. Overall, tripping the laminar layer in this way will reduce separation-bubble drag and promote the onset of turbulence which can promote maintaining attachment of the turbulent boundary layer.

But what about the entire airplane? In today's world, every attempt is made to keep surfaces smooth, contours smooth, turbulence smooth. The separation process can happen anywhere along the aircraft itself, and promote increased drag. Careful shaping of the aircraft can resolve this issue, but the design and construction work takes time, patience, and care. Take a look at this link and watch this series about what goes into making smooth work to one's favor.

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