Someone argues: "Plane Poiseuille flow becomes unstable to Tollmien-Schlichting waves at
PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Instability, transition and turbulence · Instability, transition and turbulence
Fluid Dynamics, Ch Transition to turbulence
Problem
Someone argues: "Plane Poiseuille flow becomes unstable to Tollmien-Schlichting waves at Re=Uch/ν=5772. Flow in a round pipe is just the axisymmetric version of a parallel shear flow with a similar parabolic profile, so it must also have a linear critical Reynolds number of the same order, a few thousand. Reynolds observed his dye streak break up near Re=2000, which is below 5772 but still of the right order, so this confirms that his flow crossed a linear instability threshold close to 2000."
((a)) Find the error in this reasoning.
((b)) State what is actually known about the linear stability of Hagen-Poiseuille flow, and explain in one or two sentences why turbulence nonetheless appears near Re≈2000 in ordinary pipes.