Stability for turbulent boundary layer

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SUMMARY

The discussion centers on the stability characteristics of turbulent versus laminar boundary layers in fluid dynamics. It is established that a laminar boundary layer becomes unstable when the Reynolds number exceeds the critical Reynolds number, leading to amplified perturbations. In contrast, a turbulent boundary layer, while inherently unstable, exhibits statistical stability post-transition. The transition from laminar to turbulent flow is mathematically described by the Orr-Sommerfeld eigenvalue problem.

PREREQUISITES
  • Understanding of Reynolds number and its significance in fluid dynamics
  • Familiarity with laminar and turbulent flow characteristics
  • Knowledge of boundary layer theory
  • Basic grasp of eigenvalue problems, specifically the Orr-Sommerfeld equation
NEXT STEPS
  • Study the mathematical formulation of the Orr-Sommerfeld equation
  • Explore the implications of Reynolds number on flow stability
  • Investigate the transition mechanisms from laminar to turbulent flow
  • Examine experimental methods for measuring boundary layer stability
USEFUL FOR

Fluid dynamics researchers, aerospace engineers, and anyone involved in studying flow stability and boundary layer behavior in various applications.

alsey42147
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concerning fluid flow past a body, i know that if the boundary layer is laminar then the flow becomes unstable when the Reynold's number of the flow is greater than the critical Reynold's number. is this also true when the boundary layer is turbulent?

tia
 
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I'm not quite sure what you are asking, but a turbulent boundary layer is more stable than a laminar one. Flow separation is less violent.
 
alsey42147 said:
concerning fluid flow past a body, i know that if the boundary layer is laminar then the flow becomes unstable when the Reynold's number of the flow is greater than the critical Reynold's number. is this also true when the boundary layer is turbulent?

tia

The turbulent boundary layer is unstable per-se. In a laminar boundary layer, as the Reynolds number increases, the flow becomes more unstable in the sense than any small perturbation in the flow field ends up growing above the critical Reynolds. The flow becomes unstable, all the perturbations are amplified, and after the transition to fully turbulent boundary layer the flow is unstable but statistically stable. The transition to instability of a laminar boundary layer is described mathematically as the classical eigenvalue problem so called Orr-Somerfeld.
 

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