Space-time structure around the transition point in channel flow revealed by the stochastic determinism

The transition to turbulence (Reynolds, 1883) has attracted people. Large eddy simulation (LES) and direct numerical simulation (DNS) of the transition to turbulence in straight channels employed the spatial cyclic boundary conditions between the inlet and outlet of the channel. (Moin and Kim, 1982; Kawamura and Kuwahara, 1985) Thus, these previous researches capture only the transition in time, although the spatial transition point where the laminar flow changes to turbulence could not be computed. Recently, some approaches tried to compute the transition point in straight channel for the flows having large disturbances at the inlet. (Oida and Kuwahara, 2003) However, computations of the transition points in the flows with various inlet-disturbances and also for various Reynolds numbers are still in an infant stage, although it is necessary to predict the transition points for airfoil optimizations and micro-fluids such as blood and fuel cell. Thus, we proposed the method called “stochastic determinism”, based on the deterministic Navier-Stokes equation and stochastic artificial disturbances. (Naitoh et al., 2008) Here, we show the method in detail and also clarify the space-time structure after an impulsive start for a wide range of Reynolds numbers.