Boundary layers momentum deficit

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SUMMARY

The discussion centers on the concept of "momentum deficit" in turbulent boundary layers as described in Lumley's turbulence textbook. Momentum deficit refers to the reduced momentum within the boundary layer compared to the upstream flow, primarily due to shear stresses at the wall. The turbulent eddies play a crucial role in transferring this momentum deficit away from the surface, effectively replacing it with higher momentum fluid from above. This process highlights the dynamic nature of momentum transfer in turbulent flows.

PREREQUISITES
  • Understanding of turbulent flow dynamics
  • Familiarity with boundary layer theory
  • Knowledge of shear stress concepts
  • Basic principles of fluid mechanics
NEXT STEPS
  • Study the principles of turbulent boundary layer theory
  • Explore the effects of shear stress on fluid momentum
  • Learn about momentum transfer mechanisms in turbulent flows
  • Review advanced topics in fluid dynamics using Lumley's turbulence textbook
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Engineers, fluid dynamics researchers, and students studying turbulence and boundary layer phenomena will benefit from this discussion.

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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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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.
 
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.
 

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