On the competition between centrifugal and shear instability in spiral Couette flow

The linear stability of a fluid confined between two coaxial cylinders rota ting independently and with axial sliding (spiral Couette flow) is examined . A wide range of experimental parameters has been explored, including two different radius ratios. Zeroth-order discontinuities are found in the crit ical 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-rot ating case, the centrifugal instability is dominant. Due to the competition , the neutral stability curves develop islands of instability, which consid erably lower the instability threshold. Specific and robust numerical metho ds to handle these geometrical complexities are developed. The results are in very good agreement with the experimental data available, and with previ ous computations.