This webpage accompanies our recent paper on spanwise stratified plane Couette flow; you can find a preprint here.
Stratification introduces a new spanwise/vertical lengthscale which we call the buoyancy length. This influences known large scale secondary mean flows in plane Couette flow, confining them in the spanwise direction to form flattened streamwise rolls. Associated with these rolls are layers, or sharp density gradients, near the walls and offset across the gap, where the vertical velocity and hence buoyancy flux is concentrated.
As the stratification is increased this buoyancy scale decreases (in fact it goes like U/N as expected) until is reaches the scale of the near-wall regeneration cycle of the turbulence. Specifically when it intersects the streak spacing the wall-turbulence is disrupted and the flow relaminarises.
The influence of the buoyancy length on plane Couette flow dynamics has helped us understand the formation of layers and transition to turbulence in this system.
It has also recently been shown by Facchini et. al. (2018) that the flow can undergo linear instability, provided the stratification is large enough and the domain permits certain crucial span and streamwise wavelengths.
Below the relaminarisation boundary described above, and inside the linear instability boundary this means that there opens up a new route for small perturbations to seed the previously subcritical wall-turbulence:
Above the relaminarisation boundary the linear modes saturate and initiate shear instability, but now the overturns are unable to seed wall-turbulence due to the buoyancy length disrupting the regeneration mechanism. Now the overturns become recurrent episodes with some impression of transient growth of streaky flow:
An image from this paper was used on the cover of issue 868 of the Journal of Fluid Mechanics