Layer formation and relaminarisation in plane Couette flow with spanwise stratification

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).

arXiv commentAccepted for publication at JFM

References in corpus (4)

• Stability of density-stratified viscous Taylor-Couette flows
• Layer formation in horizontally forced stratified turbulence: connecting exact coherent structures to linear instabilities
• Large scale flows in transitional plane Couette flow: a key ingredient of the spot growth mechanism
• The linear instability of the stratified plane Couette flow

Cited by in corpus (5)

• Structured input-output analysis of stably stratified plane Couette flow
• Staircase solutions and stability in vertically confined salt-finger convection
• Stably stratified exact coherent structures in shear flow: the effect of Prandtl number
• Localized layers of turbulence in stratified horizontally sheared Poiseuille flow
• Two regimes of dilute turbulent settling suspensions under shear