Derivation of Kutta Joukowski condition

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Discussion Overview

The discussion revolves around the derivation of the Kutta Joukowski condition from the Navier-Stokes equations, particularly in the context of vanishing viscosity. Participants explore the theoretical underpinnings and implications of this condition in fluid dynamics, referencing literature and related concepts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether the Kutta Joukowski condition can be derived from the Navier-Stokes equations in the limit of vanishing viscosity and seeks relevant literature.
  • Another participant suggests Wikipedia as an introductory resource, although it is noted that the original inquiry pertains specifically to the Kutta condition rather than the theorem.
  • A third participant recommends a book titled "Principles of Ideal Flow Gas Dynamics" by Karamcheti, which addresses the mathematics and theory of ideal flows, including the Kutta-Joukowski condition.
  • A later reply discusses the construction of physically correct solutions to the frictionless Burgers equation in the context of weak solutions and entropy production, proposing a potential analogy to minimizing entropy in the Kutta condition scenario.
  • Concerns are raised about the behavior of velocity at a sharp trailing edge in inviscid flow and the implications of introducing viscosity, particularly regarding entropy generation.

Areas of Agreement / Disagreement

Participants express differing views on the derivation and implications of the Kutta Joukowski condition, with no consensus reached on the specific methods or interpretations discussed.

Contextual Notes

The discussion touches on complex concepts such as weak solutions, entropy production, and the behavior of velocity in inviscid versus viscous flows, which may require further clarification and exploration of assumptions involved.

DrDu
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Can the Kutta Joukowski condition be derived from the Navier Stokes equations in the limit of vanishing viskosity?
Is there some literature on this point?
 
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More specifically: I was reading on how physically correct solutions to the frictionless Burgers equation are constructed when a shock appears as "weak solutions" of the general equation in the limit of vanishing viscosity. Entropy is then only generated at the shocks and searching for a solution which minimizes entropy production leads to the correct result. In easy two dimensional air foil problems one only has to fix the value of rotational flow. I wonder whether this can not also be reduced to a problem of minimizing entropy.
In the inviscid flow the velocity becomes infinite at a sharp trailing edge for almost all values of the rotation. If a small viscosity is introduced, velocity is no longer infinite but there would probably a lot of entropy be generated.
 

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