We investigate the linear stability of shears near Couette flow for a class 2D incompressible stably stratified fluids. Our main result consists nearly optimal decay rates perturbations stationary states whose velocities are monotone shear flows $(U(y),0)$ and have an exponential density profile. In case $U(y)=y$, we recover predicted by Hartman in 1975, adopting explicit point-wise approach fr...

We study numerically shear banded flow in planar and curved Couette geometries. Our aim is to capture two recent observations in shear banding systems of roll cells stacked in the vorticity direction, associated with an undulation of the interface between the bands. Depending on the degree of cell curvature and on the material's constitutive properties, we find either (i) an instability of the ...

The transition to turbulence in pipe and plane Couette flow differs from the better understood situation of Taylor-Couette or Rayleigh-Bénard flow in that the laminar profile is stable against infinitesimal perturbations for all Reynolds numbers. Moreover, even when turbulent flow is established, it can spontaneously return to laminar flow. These observations are compatible with the formation o...

Cell exclusion is the phenomenon whereby the hematocrit and viscosity of blood decrease in areas of high stress. While this is well known in naturally occurring Poiseuille flow in the human body, it has never previously been shown in Couette flow, which occurs in implantable devices including blood pumps. The high-shear stresses that occur in the gap between the boundaries in Couette flow are k...

Matched asymptotic solutions for the steady banded flow of the diffusive Johnson-Segalman model in various geometries ⋆ Abstract We present analytic solutions for steady flow of the Johnson-Segalman (JS) model with a diffusion term in various geometries and under controlled strain rate conditions , using matched asymptotic expansions. The diffusion term represents a singular perturbation that l...