Turbulent–laminar patterns in shear flows without walls

Matthew Chantry (1) , Laurette S. Tuckerman (1) , Dwight Barkley (2)

1 PMMH - Physique et mécanique des milieux hétérogenes (UMR 7636)
2 Mathematics Institute [Warwick]

Turbulent-laminar intermittency, typically in the form of bands and spots, is a ubiquitous feature of the route to turbulence in wall-bounded shear flows. Here we study the idealised shear between stress-free boundaries driven by a sinusoidal body force and demonstrate quantitative agreement between turbulence in this flow and that found in the interior of plane Couette flow – the region excluding the boundary layers. Exploiting the absence of boundary layers, we construct a model flow that uses only four Fourier modes in the shear direction and yet robustly captures the range of spatio-temporal phenomena observed in transition, from spot growth to turbulent bands and uniform turbulence. The model substantially reduces the cost of simulating intermittent turbulent structures while maintaining the essential physics and a direct connection to the Navier-Stokes equations. We demonstrate the generic nature of this process by introducing stress-free equivalent flows for plane Poiseuille and pipe flows which again capture the turbulent-laminar structures seen in transition.

Mots clés: low-dimensional models; pattern formation; transition to turbulence

Domaines: Physique [physics]; Mathématiques [math]

Matthew Chantry, Laurette S. Tuckerman, Dwight Barkley. Turbulent–laminar patterns in shear flows without walls. Journal of Fluid Mechanics, 2016, 791, pp.R8. ⟨10.1017/jfm.2016.92⟩. ⟨hal-01293035⟩