# Would there be turbulence around objects w/o boundary layers

## Main Question or Discussion Point

According to wikipedia "The onset of turbulence can be predicted by the Reynolds number, which is the ratio of inertial forces to viscous forces within a fluid which is subject to relative internal movement due to different fluid velocities, in what is known as a boundary layer in the case of a bounding surface such as the interior of a pipe".
I might be misunderstanding, but one takeaway from this is that if there was no boundary layer around an hypothetical object (i.e. it would repell air molecules), then there would be no velocity difference between the layers of air and consequently no turbulenece. Is that correct? Is the velocity difference between the "layers" of air the cause for turbulence?

## Answers and Replies

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anorlunda
Mentor
Traditionally, we think of a layer of laminar flow at the confining wall. Further away from the wall there might be turbulent flow. The boundary layer is between them. https://en.wikipedia.org/wiki/Boundary_layer

But nanotechnology is upsetting some of those traditional beliefs. Especially hydrophobic surfaces. Saying that they repel "all molecules" is overstating it. but some molecules yes.

boneh3ad
Science Advisor
Gold Member
Traditionally, we think of a layer of laminar flow at the confining wall. Further away from the wall there might be turbulent flow. The boundary layer is between them. https://en.wikipedia.org/wiki/Boundary_layer
This is not correct. In general, the flow around/over an object or surface can be modeled using inviscid flow over most of the domain. The exception is the region very close to the surface where viscosity is important. This entire region where viscosity is important is the boundary layer. Intuitively, it is the region of the flow where the velocity is zero (relative to the surface) where it touches the surface, and is the same as the free-stream velocity at the upper extreme. This requires no knowledge a priori about the laminar/turbulent state of the boundary layer.

"The onset of turbulence can be predicted by the Reynolds number, which is the ratio of inertial forces to viscous forces within a fluid which is subject to relative internal movement due to different fluid velocities, in what is known as a boundary layer in the case of a bounding surface such as the interior of a pipe".
Before we go any further, I would caution anyone reading this into taking the Wikipedia article at face value. The onset of turbulence, in general, cannot actually be predicted. We know that a higher Reynolds number ($Re$) means we are more likely to see turbulence, but in most cases, there is no foolproof predictive metric.

I might be misunderstanding, but one takeaway from this is that if there was no boundary layer around an hypothetical object (i.e. it would repell air molecules), then there would be no velocity difference between the layers of air and consequently no turbulenece. Is that correct? Is the velocity difference between the "layers" of air the cause for turbulence?
As far as I know, there is no reason to believe that there is some magical surface that would "repel air molecules" in a way that there would be no boundary layer. Even if this was possible, there are fundamentally two things that are required for turbulence: an energy source and viscosity. You haven't eliminated those, so turbulence is still theoretically possible. One possible manifestation of this would be in the wake of the object.

As boneh3ad pointed out you need viscosity so you need shear flow (velocity gradient). This can occur without a boundary layer. For example a jet of air at high speed relative to the surrounding air. Shear is generated in the atmosphere all the time due to gradients in the wind velocity which can be caused by a variety of factors such as temperature gradients.