Abstract The shear–driven, bilayer flow of two immiscible liquids sandwiched between a moving planar and stationary corrugated plate, in parallel alignment under Stokes conditions, is explored. motivation, partly inspired by biomimetic considerations, the use surface texturing/topography to reduce friction wear while increasing load carrying capacity lubrication problems. starting point associa...

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Unsteady hydromagnetic generalised Couette flow of a viscous, incompressible and electrically conducting fluid between two horizontal parallel porous plates Darcian channel in the presence of a uniform transverse magnetic field taking Hall current and ion-slip into account in a rotating system is investigated. An exact solution of the governing equations is obtained by Laplace transform techniq...

Despite the importance of the magnetorotational instability (MRI) as a fundamental mechanism for angular momentum transport in magnetized accretion disks, it has yet to be demonstrated in the laboratory. A liquid sodium αω dynamo experiment at the New Mexico Institute of Mining and Technology provides an ideal environment to study the MRI in a rotating metal annulus (Couette flow). A local stab...

Plane Couette ow perturbed by a spanwise oriented ribbon, similar to a con guration investigated experimentally at CEA-Saclay, is investigated numerically using a spectral-element code. 2D steady states are computed for the perturbed con guration; these di er from the unperturbed ows mainly by a region of counter-circulation surrounding the ribbon. The 2D steady ow loses stability to 3D eigenmo...

A nonlinear stability analysis by Demay and looss [J. Mec. Theor. Appl. , special issue, p. 193 (1984)] of flow between concentric rotating cylinders (the Couette-Taylor system) predicted a transition from the basic flow to a state with ribbons, which are traveling waves in the azimuthal direction but standing waves in the axial direction. We have observed the transition to ribbons in laborator...

We discuss the problem of deriving estimates for the resolvent of the linear operator associated with three dimensional perturbations of plane Couette flow, and determining its dependence on the Reynolds number R. Depending on the values of the parameters involved, we derive estimates analytically. For the remaining values of the parameters, we prove that deriving estimates for the resolvent ca...

The linear marginal instability of an axisymmetric MHD Taylor-Couette flow of infinite vertical extension is considered. For flows with a resting outer cylinder there is a well-known characteristic Reynolds number even without magnetic field but for sufficiently weak magnetic fields there are solutions with smaller Reynolds numbers so that a characteristic minimum exists. The minimum only exist...

Chaotic transport and mixing in wavy cylindrical Couette flow has been studied in some detail, but previous studies have been limited to the velocity field at transition from Taylor–Couette flow to wavy flow or have used phenomenological, computational, or theoretical models of the flow. Recent particle image velocimetry measurements of wavy vortex flow provide the experimental three-dimensiona...