FLOW IN A CYLINDER DRIVEN BY ROTATING SPLIT-DISK ENDWALLS

Flow of an incompressible viscous fluid contained in a cylindrical ves sel (radius R, height H) is considered. Each of the cylinder endwalls is split into two parts which rotate steadily about the central axis w ith different rotation rates: the inner disk (r < r1) rotating at OMEG A1, and the outer annulus (r, < r < R) rotating at OMEGA2. Numerical s olutions to the axisymmetric Navier-Stokes equations are secured for s mall system Ekman numbers E (= nu/(OMEGAH-2)). In the linear regime, w hen the Rossby number Ro ( = 2(OMEGA2 - OMEGA1)/(OMEGA1, + OMEGA2)) mu ch less than 1, the numerical results are shown to be compatible with the theoretical prediction as well as the available experimental measu rements. Emphasis is placed on the results in the nonlinear regime in which Ro is finite. Details of the structures of azimuthal and meridio nal flows are presented by the numerical results. For a fixed Ekman nu mber, the gross features of the flow remain qualitatively unchanged as Ro increases. The meridional flows are characterized by two circulati on cells. The shear layer is a region of intense axial flow toward the endwall and of vanishing radial velocity. The thicknesses of the shea r layer near r = r1 and the Ekman layer on the endwall scale with E1/4 and E1/2, respectively. The numerical results are consistent with the se scalings.