Patterns in transitional shear flows. Part 2: Nucleation and optimal spacing

S. Gomé, L. S. Tuckerman, D. Barkley

Published 2022-11-28Version 1

Low Reynolds number turbulence in wall-bounded shear flows en route to laminar flow takes the form of oblique localised turbulent structures. These emerge from uniform turbulence via a spatiotemporal intermittent process in which localised quasi-laminar gaps randomly nucleate and disappear. For slightly lower Reynolds numbers, periodic and approximately stationary laminar-turbulent patterns predominate. The statistics of quasi-laminar regions are analysed in several respects, including the distributions of space and time scales and their Reynolds number dependence. A smooth, but marked transition is observed between uniform turbulence and flow with intermittent quasi-laminar gaps, while the transition from gaps to patterns is more gradual. Wavelength selection in these patterns is analysed via numerical simulations in oblique domains of various sizes. Lifetime measurements in a minimal domain demonstrate the existence of a preferred wavelength. Wavelet transforms are performed on turbulent-laminar patterns, measuring areas and times over which a given wavelength dominates in a large domain. This leads to the quantification of the stability of a pattern as a function of wavelength and Reynolds number. We report that the preferred wavelength maximises the energy and dissipation of the large-scale flow along laminar-turbulent interfaces. This optimal behaviour is primarily due to the advective nature of this large-scale flow, while the role of turbulent fluctuations is secondary in the wavelength selection.