Supercomputing of transition to turbulence in pipe with adit flow

Transition from laminar flow to turbulence often occurs in closed pipes such as pathologic blood vessels and artificial systems such as micro-tubes. While varying disturbances entering at pipe inlet or at heart pump, the transition points in space from laminar flow to turbulence in closed pipe are solved by using the weakly-stochastic Navier-Stokes equation and a finite difference method proposed previously by us (Naitoh and Shimiya, 2011), although the previous numerical simulations and instability theories based on the deterministic Navier-Stokes equation could never indicate the transition point in closed tunnel. The most important point of our approach is a philosophical method proposed for determining the stochasticity level, which is deeply related to boundary condition. Here, we qualitatively clarify the relation between the transition point and amount of adit on solid wall, because living systems exchange water and molecules through the wall of blood vessel. A mysterious feature obtained is that a larger amount of additional adit at the inlet may result in laminalization of the boundary layer.