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Stability theory (Boundary Layer)

  1. Apr 15, 2014 #1
    Hi all. I am new to boundary layers. Do the stability region of viscous Laminar and inviscid flow overlap? Why?

    Thanks :)
     
  2. jcsd
  3. Apr 15, 2014 #2
  4. Apr 15, 2014 #3

    boneh3ad

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    Assuming you are talking about the stability of a boundary layer as it pertains to the transition process, this is quite a complex topic and you have to be careful with your terminology here. In a boundary layer, the concept of inviscid flow makes no sense. Without viscosity, there would be no boundary layer. On the other hand, it is common practice to sometimes consider what is called "inviscid instability" where viscosity's effect on the generation of unstable waves in the flow is neglected but it's effect on the overall flow in generating a boundary layer profile is still considered (or else there would be no stability problem).

    If this is the concept to which you are referring, then your question is a bit vague. In wavenumber-Reynolds number space, the two curves will frequently overlap, though the region of viscous instability is typically much smaller. Inviscid waves, sometimes called Rayleigh waves, are very unstable and grow rapidly toward turbulent breakdown. The effects of viscosity, however, are highly stabilizing to these waves, so when viscosity is considered, their unstable region tends to shrink. On the other hand, viscosity, through its generation of Reynolds shear stresses, introduces it own mechanisms of instability, e.g. Tollmien-Schlichting waves on a flat plate.
     
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