On the competition between centrifugal and shear instability in spiral Couette flow
Abstract
The linear stability of a fluid confined between two coaxial
cylinders rotating independently and with axial sliding (Spiral Couette
flow) is examined. A wide range of experimental parameters has been
explored, including two different radius ratios. Zeroeth order
discontinuities are found in the critical surface; they are explained as a
result of the competition between the centrifugal and shear instability
mechanisms, which appears only in the co--rotating case, close to the
rigid body rotation region. In the counter--rotating case, the centrifugal
instability is dominant. Due to the competition, the neutral stability
curves develop islands of instability, which considerably lower the
instability threshold. Specific and robust numerical methods to handle
these geometrical complexities are developed. The results are in very
good agreement with the experimental data available, and with previous
computations.
