Generalization of Landau's criterion for Hagen–Poiseuille flow instability

The generalization of the Feynman modification of Landau's (1941) superfluid criterion, which gives the Reynolds number threshold condition Re>Reth≈1976 for the energetically favorable creation of small thin vortex rings in the boundary layer of the classical laminar Hagen–Poiseuille (HP) flow, is stated. This condition of the HP flow instability is not dependent on the infinitesimal perturbation energy, as usual in the linear instability theory, and is consistent with a sharp increase in the pipe drag coefficient and with the observational data for puff formation in the HP flow. The explicit analytical solutions for the pipe drag coefficient and for the viscous diffusion of vorticity in shear flows are obtained. The latter solution describes the dissipation and production rates of perturbation energy near the wall of the pipe and the characteristic time for the HP flow instability realization. That solution meets with the vortex burst periods observed in the boundary layer and with known observational data on the dissipation and production rates for the turbulent flow energy in the pipe and in the boundary layer.