Linear and nonlinear instabilities of sliding Couette flow

Abstract

We consider an incompressible viscous fluid with the kinematic viscosity v between two infinitely long concentric cylinders with radii a and b (b > a). The fluid experiences a shear motion produced by pulling the inner cylinder with the axial speed U while keeping the outer cylinder at rest (see Fig.1). The axial basis flow at the radius r,

$$U_{B}(r) = R\frac{\ln(r(1 - \eta)/2)}{\ln(\eta)},$$

can be obtained as an exact solution of the Navier-Stokes equation, where $R = U(b - a)/2v$ is the Reynolds number and $\eta = a/b$ is the radius ratio.