Derivation of Kutta Joukowski condition

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SUMMARY

The Kutta Joukowski condition can be derived from the Navier-Stokes equations in the limit of vanishing viscosity, as discussed in the forum. The conversation highlights the importance of understanding the Kutta condition, particularly in relation to the frictionless Burgers equation and the generation of entropy at shocks. Key literature includes "Principles of Ideal Flow Gas Dynamics" by Karamcheti, which provides a mathematical foundation for ideal flows. The discussion emphasizes the relationship between minimizing entropy production and achieving correct solutions in inviscid flow scenarios.

PREREQUISITES
  • Understanding of Navier-Stokes equations
  • Familiarity with Kutta condition and Kutta-Joukowski theorem
  • Knowledge of the frictionless Burgers equation
  • Concept of entropy production in fluid dynamics
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  • Research the derivation of the Kutta Joukowski condition from Navier-Stokes equations
  • Study the principles outlined in "Principles of Ideal Flow Gas Dynamics" by Karamcheti
  • Explore the concept of weak solutions in the context of the frictionless Burgers equation
  • Investigate methods for minimizing entropy production in fluid dynamics
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Fluid dynamicists, aerospace engineers, and researchers interested in the mathematical foundations of ideal flows and entropy production in inviscid flow scenarios.

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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