Boundary layers momentum deficit

In summary, Lumley's textbook on turbulence discusses the transfer of momentum deficit away from the surface in turbulent boundary layers. This refers to the decrease in momentum within the boundary layer due to shear stresses at the wall. The author uses the term "momentum deficit" to describe all momentum within the boundary layer. In turbulent conditions, there is significant transfer of momentum in all directions, with low momentum fluid being transported away from the surface and replaced by higher momentum fluid from above.
  • #1
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Lumley, turbulence textbook on boundary layers, introduction pages:

"The turbulent eddies transfer momentum deficit away from the surface".

Can anyone explain what this means, specifically what is momentum deficit? In my mind, the word "deficit" means a shortage of something, so how can one write that a shortage of something is transferred somewhere?

This lecture also has the phrase "momentum deficit" but doesn't explain it:
http://www.bakker.org/dartmouth06/engs150/11-bl.pdf
 
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  • #2
Ok, well my interpretation of it is that quite simply, the momentum inside a boundary layer is called "momentum deficit", that is, relative to the upstream flow, there is less momentum in the boundary layer due to shear stresses at the wall. So the author, I believe, simply refers to all momentum in the boundary layer as "momentum deficit". In turbulent boundary layers, we then have significant transfer of momentum in all directions and I think this is what is implied by the author in the above quote.
 
  • #3
The author means that the low momentum fluid is transported away from the surface and replaced by fluid with more momentum that came from above the surface.
 

1. What is a boundary layer momentum deficit?

A boundary layer momentum deficit is a phenomenon that occurs in fluid dynamics, specifically in the study of boundary layers. It refers to the decrease in momentum or energy of a fluid flow near a solid surface, due to the presence of viscous forces. This deficit can be observed in various fluid flow situations, such as air flow over an airplane wing or water flow near a boat hull.

2. How is boundary layer momentum deficit calculated?

The boundary layer momentum deficit is typically quantified using the concept of boundary layer thickness. This is the distance from the solid surface at which the velocity of the fluid flow is significantly reduced compared to the free stream velocity. The momentum deficit can then be calculated by comparing the velocity profiles at different distances from the surface.

3. What are the factors that affect boundary layer momentum deficit?

Several factors can influence the magnitude of the boundary layer momentum deficit, including the fluid viscosity, the speed of the flow, and the surface roughness. Other factors such as the angle of attack, surface curvature, and fluid density can also play a role in determining the extent of the momentum deficit.

4. How does boundary layer momentum deficit impact aircraft design?

Boundary layer momentum deficit is a crucial consideration in aircraft design, as it can affect the aerodynamic performance and efficiency of an aircraft. Designers must carefully consider the shape and surface characteristics of the aircraft to minimize the momentum deficit and reduce drag, thereby improving fuel efficiency and flight performance.

5. Can boundary layer momentum deficit be eliminated?

While it is not possible to completely eliminate boundary layer momentum deficit, it can be reduced through various techniques. These include using specialized surface treatments, such as riblets or vortex generators, to manipulate the boundary layer and reduce its thickness. Other methods, such as suction or blowing, can also be employed to control the momentum deficit. However, these techniques must be carefully balanced with other design considerations to achieve optimal performance.

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