Layer formation and relaminarisation in plane Couette flow with spanwise stratification

TL;DR

This study explores how spanwise stratification and rigid boundaries influence layer formation, flow structures, and transition to turbulence in plane Couette flow, revealing new coherent structures and stability mechanisms.

Contribution

It extends previous work by analyzing the effects of spanwise stratification and boundaries on flow dynamics, identifying new layered structures and their role in turbulence transition.

Findings

Observation of near-wall layering and large scale spanwise-flattened streamwise rolls.

Layer buoyancy scaling law $l_z o U/N$ confirmed.

Identification of stratified modifications to large scale secondary flows.

Abstract

Recent research has shed light on the role of coherent structures in forming layers when stably stratified turbulence is forced with horizontal shear (Lucas, Caulfield & Kerswell, J. Fluid Mech., vol. 832, 2017, pp. 409-437). Here we extend our previous work to investigate the effect of rigid boundaries on the dynamics by studying stably-stratified plane Couette flow with gravity oriented in the spanwise direction. We observe near-wall layering and associated new mean flows in the form of large scale spanwise-flattened streamwise rolls. The layers exhibit the expected buoyancy scaling $l_z\sim U/N$ where $U$ is a typical horizontal velocity scale and $N$ the buoyancy frequency. We associate the new coherent structures with a stratified modification of the well-known large scale secondary flow in plane Couette and find that the possibility of the transition to sustained turbulence is controlled by the relative size of this buoyancy scale to the spanwise spacing of the streaks. We also investigate the influence on the transition to turbulence of the newly discovered linear instability in this system (Facchini et. al. 2018 arXiv:1711.11312).