Reynold's Equation: Navier-Stokes to Const. Density Flow

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SUMMARY

The discussion centers on deriving Reynold's Equation from the Navier-Stokes Equation for incompressible flow with constant density. Reynold's Equation represents the time-averaged Navier-Stokes Equation, emphasizing the velocity field's randomness. A critical component of this derivation is the "Reynolds' stress tensor," which accounts for the non-linear interactions of random perturbations influencing the averaged velocity field.

PREREQUISITES
  • Understanding of Navier-Stokes Equations
  • Familiarity with incompressible flow concepts
  • Knowledge of Reynolds' stress tensor
  • Basic principles of fluid dynamics
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  • Study the derivation of Reynold's Equation from the Navier-Stokes Equation
  • Explore the concept of Reynolds' stress tensor in detail
  • Investigate applications of Reynold's Equation in turbulence modeling
  • Learn about time-averaging techniques in fluid dynamics
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Fluid dynamicists, researchers in turbulence modeling, and students studying advanced fluid mechanics will benefit from this discussion.

mekrob
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Hi,

I've been asked to turn the Navier-Stokes Equation (incompressible flow, constant density) into the Reynold's Equation. However, I can't find the Reynold's equation in my notes or book. I don't need help solving the problem, I just need to know the end result, otherwise I have no idea what I'm working towards.

Thanks.
 
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Reynold's equation is the time-averaged N-S equation when we explicitly regard the velocity field as random.
The main feature that will pop up will be "Reynolds' stress tensor", which is, in essence, the non-linear products of the random perturbations that affects the evolution of the avereged velocity field.
 

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