Stability of Couette flow between free cylinders with allowance for self- gravitation
The two-dimensional system described here consists of two rotating cylinders whose centres are free to move in a plane perpendicular to the axis of rotation, with an incompressible fluid in irrotational motion between them, subject to self-gravitation. The classical problem of Couette flow stability is augmented by the gravitational forces and the possibility of motion of the centres of the cylinders. Complex variable methods are used to derive two second order differential equations for the complex positions of the centres of the cylinders. The curves of neutral stability are calculated from the discriminant of the equations, where it is found that the ratio of the density of the inner cylinder to the density of the fluid is an important parameter in the stability diagram.
scientific article; zbMATH DE number 515018