A BIFURCATION STUDY OF VISCOUS-FLOW THROUGH A ROTATING CURVED DUCT

The combined effects of system rotation (Coriolis force) and curvature (centrifugal force) on the bifurcation structure of two-dimensional f lows in a toroidal geometry of rectangular cross-section are examined. The problem depends on the Rossby number, R0 = U/bOMEGA, the Ekman nu mber, Ek = nu/b2OMEGA, the aspect ratio, gamma = b/h and the radius ra tio, eta = r(i)/r(o); here U is the velocity scale, b is the channel w idth in the spanwise direction, OMEGA is the rotational speed, (r(i), r(o)) are the inner and outer radii of the duct, h = r(o) - r(i) is th e channel gap in the radial direction and nu is the kinematic viscosit y of the fluid. A pseudospectral method is devised to discretize the t wo-dimensional Navier-Stokes equation in stream-function form. Continu ation schemes are used to track the solution paths with Rossby number as the control parameter. Extended systems are used to determine the p recise location of the singular points of the discretized system. The loci of such singular points are tracked with respect to curvature of the duct. Unlike the findings of Miyazaki (1973) on the same problem, curvature is found to have profound effects on the solution structure; flow mutations take place through a tilted cusp at (Ro = 7.122, eta = 0.678) and a transcritical bifurcation point at (Ro = 1.357, eta = 0. 349).