The transition to turbulence (broadly-defined Tollmien-Schlichting wave) and re-laminariation phenomenon of compressible and incompressible flows in straight-channels of square and rectangular cross-sections are simulated by three-dimensional unsteady computational fluid dynamics without any instability theories. We propose the governing equation averaged in the volume of the characteristic scale smaller than that for continuum mechanics: the stochastic Navier-Stokes equation lying at the triple point of the Boltzmann, the Langevin, and Schrodinger equations. Stochasticity comes from the molecular discontinuity. An important point is that a new type of indeterminacy principle, which differs from that for quantum mechanics, makes it possible to predict the transition points in space for varying Reynolds numbers, Mach numbers, and inlet disturbances. Transition points in space, turbulence intensities, and mean velocity profiles computed are compared with some experiments. We will also propose two different types of computational methods of the stochastic terms.
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