Sixth International Symposium on Turbulence and Shear Flow Phenomena Seoul, Korea, 22-24 June 2009 SPACE-TIME STRUCTURE AROUND THE TRANSITION POINT IN CHANNEL FLOW REVEALED BY THE STOCHASTIC DETERMINISM Hiromu Shimiya Faculty of Science and Engineering, Waseda University 3-4-1 Ookubo, Shinjuku-ku, Tokyo, 169-8555, Japan Ken Naitoh Faculty of Science and Engineering, Waseda University 3-4-1 Ookubo, Shinjuku-ku, Tokyo, 169-8555, Japan
[email protected] ABSTRACT difference method extended based on the multi-level The transition to turbulence (Reynolds, 1883) has formulation (Naitoh and Kuwahara, 1992), which can attracted people. Large eddy simulation (LES) and direct calculate spatial derivatives of physical quantities and numerical simulation (DNS) of the transition to turbulence integrated quantities accurately, leads us to the new stage of in straight channels employed the spatial cyclic boundary computational fluid dynamics. conditions between the inlet and outlet of the channel. Starting point of the methodology is related to the equation (Moin and Kim, 1982; Kawamura and Kuwahara, 1985) of the divergence of velocity in the multi-level formulation, Thus, these previous researches capture only the transition which is transformed from the compressible Navier-Stokes in time, although the spatial transition point where the equation while maintaining the Gibbs formula. (Naitoh and laminar flow changes to turbulence could not be computed. Kuwahara, 1992.) The formulation shows that the second Recently, some approaches tried to compute the transition derivative of velocity, the divergence of velocity, controls point in straight channel for the flows having large the physical quantities such as pressure, velocity, and disturbances at the inlet.