Thomas Ward, Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, CA 90095-1555 and William Hourigan, Mechanical and Aerospace Engineering, University of California, Los Angeles, Engineering IV, Los Angeles, CA 90095-1597.
A tilted-partially filled rotating tank is studied experimentally at O(1) Reynolds and small $<1$ capillary numbers, to study mixing of a viscous homogeneous fluid. Of particular interest is the transition from the low Reynolds number flow, that exhibits two large vortices, to the laminar flow regime which results in additional vortex generation. In the low Reynolds number (<<1) limit, a nonlinear analysis (Ward & Metchik, Chem. Engng. Sci., 2007)predicted that the two vortex generation case and rate of mixing are possibly generated by a periodic shear type instability (Franjione & Ottino, Trans. Phil. R. Soc., 1992). As the Reynolds number increases to the laminar regime, the two vortices show some interactions with the walls and begin a cascading effect that is similar to the well known Moffatt (J. Fluid Mech., 1964) vortices in Stokes flow in cavities. The additional vortices aid in transporting material from the liquid rotation axis, and the walls, to the bulk of the region between them. But the vortices also intensify in magnitude with increasing rotation rate leading to the appearance of KAM surfaces, which are barriers to efficient mixing. Experiments are performed using a 90% glycerol/water mixture at two volume portions with angles ranging between 25o to 65o measured from thee horizontal. Laser fluorescence is used to illuminate the vortices via experimental Poincaré mapping experiments are performed to examine the mixing patterns via experimental Poincaré mapping (Fountain, Khakhar & Ottino, Science, 1998), and the resulting images are analyzed to determine the mixed cross sectional area versus elapsed time.