Final stages of transition to turbulence in plane channel flow

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Abstract
This paper involves a numerical simulation of the final stages of transition to turbulence in plane channel flow at a Reynolds number of 1500. Three-dimensional incompressible Navier–Stokes equations are numerically integrated to obtain the time evolution of two- and three-dimensional finite-amplitude disturbances. Computations are performed on the CYBER-203 vector processor for a 32 × 51 × 32 grid. Solutions indicate the existence of structures similar to those observed in the laboratory and characteristic of the various stages of transition that lead to final breakdown. In particular, evidence points to the formation of a A-shaped vortex and the subsequent system of horsehoe vortices inclined to the main flow direction as the primary elements of transition. Details of the resulting flow field after breakdown indicate the evolution of streaklike formations found in turbulent flows. Although the flow field does approach a steady state (turbulent channel flow), the introduction of subgrid-scale terms seems necessary to obtain fully developed turbulence statistics.