Absolute and convective instabilities in creeping Couette flow with an elastic boundary.

In the zero Reynolds number limit of Stokes flow, the plane Couette flow between moving walls becomes unstable if one of the walls is covered by a layer of soft elastic solid. This instability, which has been studied experimentally and theoretically for a variety of solid constitutive laws, is triggered at the fluid-solid interface where the coupling between these two phases takes place. Considering an incompressible solid in the approximation of linear elasticity, we analytically obtain the dispersion relation in closed form. We relate the origin of the instability to the phase difference between the vertical components of the solid displacement and the fluid velocity at the interface. We then characterize the spatiotemporal properties of the instability, i.e., its absolute/convective nature in different reference frames, with a recent method whereby the imaginary part of the complex wavenumber is related to the observer's velocity by a Legendre transform.