Loss of stability in Couette flow at different Rossby numbers

The stability problem for a flow of a viscous incompressible liquid between two coaxial rotating cylinders is formulated in cylindrical coordinates using a nonstationary Navier-Stokes system. Only periodic flows with a period of 2pi/alpha are considered, and the stability problem is reduced to a series of spectral problems for ordinary differential operators. These are solved by using an algorithm proposed in earlier studies (Babenko et al., 1981, 1982). The results obtained have made it possible to identify two regions with axisymmetric and nonaxisymmetric bifurcation, respectively.