An approach for finding quantum leap of drag reduction: Based on the weakly-stochastic Navier-Stokes equation

While varying inlet disturbances, the transition points in space from laminar flow to turbulence in pipes and on airfoil in wind tunnel are here solved by using the weakly-stochastic Navier-Stokes equation and a finite difference method proposed by us, although the previous numerical simulations and instability theories based on the deterministic Navier-Stokes equation could not indicate the transition point in closed pipe flow. The most important point of our approach is a theoretical and philosophical method proposed for determining the stochasticity level, which is deeply related to boundary condition. Independence of the transition point on grid size implies that stochasticity is dominant rather than numerical discretization. Moreover, we qualitatively clarify the relation between the transition point and amount of adit on solid wall. Thus, the present approach will lead to a new way for reducing drag force.