For small viscosity, exact Tollmien-Schlichting wave solutions exist for wavenumbers from ν^{1/8} to ν^{1/12}, with imaginary phase speed crossing zero at the lower and upper neutral branches.
Instability of shear layers and Prandtl's boundary layers
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This paper is devoted to the study of the nonlinear instability of shear layers and of Prandtl's boundary layers, for the incompressible Navier Stokes equations. We prove that generic shear layers are nonlinearly unstable provided the Reynolds number is large enough, or equivalently provided the viscosity is small enough. We also prove that, generically, Prandtl's boundary layer analysis fails for initial data with Sobolev regularity. In both cases we give an accurate description of the first instability which arises. In some cases a secondary instability appears, leading to several sublayers and to an unexpected complexity of the flow.
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Tollmien-Schlichting waves near neutral stable curve
For small viscosity, exact Tollmien-Schlichting wave solutions exist for wavenumbers from ν^{1/8} to ν^{1/12}, with imaginary phase speed crossing zero at the lower and upper neutral branches.