Linear stability of the cylindrical Couette flow of a rarefied gas

Abstract

A rarefied gas between two coaxial circular cylinders of infinite length, rotating with different angular velocities and kept at a common temperature, is considered. The stability of the circumferentially as well as axially uniform flow (cylindrical Couette flow) for circumferentially uniform small disturbances is investigated on the basis of kinetic theory. The linear-stability analysis is performed using the Bhatnagar-Gross-Krook model of the Boltzmann equation and the diffuse reflection condition on the cylinders. The maximum growth rate of the disturbances is determined numerically by solving the initial and boundary value problem for the disturbances for relatively small Knudsen numbers and wide ranges of angular velocities of the cylinders. As a result, the parameter range where the cylindrical Couette flow is unstable is clarified. The result is compared with the corresponding result based on the continuum model of the compressible Navier-Stokes type. A comparison is also made with the result of a direct numerical analysis of the original Boltzmann system, obtained by the direct simulation Monte Carlo method in previous papers as well as in the present study.