Theoretical conditions of pipe flow transition: new approach to the old   problem
  For Hagen-Poiseuille flow the mechanism of laminar-to-turbulent transition originated from the deceleration of disturbed streams on the pipe wall is analyzed. An expression for the critical Reynolds number and the disturbance in the form of ring obstacle is derived. The good qualitative agreement between the theoretical results and published experimental data is demonstrated 
Andrei Nechayev
physics.flu-dyn