Direct numerical simulation of a turbulent Couette-Poiseuille flow, part 2: Large- and very-large-scale motions

Abstract

A direct numerical simulation dataset of a fully developed turbulent Couette-Poiseuille flow is analyzed to investigate the spatial organization of streamwise velocity-fluctuating u-structures on large and very large scales. Instantaneous and statistical flow fields show that negative-u structures with a small scale on a stationary bottom wall grow throughout the centerline due to the continuous positive mean shear, and they penetrate to the opposite moving wall. The development of an initial vortical structure related to negative-u structures on the bottom wall into a large-scale hairpin vortex packet with new hairpin vortices, which are created upstream and close to the wall, is consistent with the auto-generation process in a Poiseuille flow (Zhou et al., J. Fluid Mech., vol. 387, 1999, pp. 353-396). Although the initial vortical structure associated with positive-u structures on the top wall also grows toward the bottom wall, the spatial development of the structure is less coherent with weak strength due to the reduced mean shear near the top wall, resulting in less turbulent energy on the top wall. The continuous growth of the structures from a wall to the opposite wall explains the enhanced wall-normal transport of the streamwise turbulent kinetic energy near the centerline. Finally, an inspection of the time-evolving instantaneous fields and conditional averaged flow fields for the streamwise growth of a very long structure near the centerline exhibits that a streamwise concatenation of adjacent large-scale u-structures creates a verylarge-scale structure near the channel centerline.