Nonlinear vortex development in rotating flows

Abstract

We present the results of a combined experimental and numerical investigation into steady secondary vortex flows confined between two concentric right circular cylinders. When the flow is driven by the symmetric rotation of both end walls and the inner cylinder, toroidal vortex structures arise through the creation of stagnation points (in the meridional plane) at the inner bounding cylinder or on the mid-plane of symmetry. A detailed description of the flow regimes is presented, suggesting that a cascade of such vortices can be created. Experimental results are reported, which visualize some of the new states and confirm the prediction that they are stable to (mid-plane) symmetrybreaking perturbations.We also present some brief results for the flows driven by the rotation of a single end wall. Vortex structures may also be observed at low Reynolds numbers in this geometry. We show that standard flow visualization methods lead to some interesting nonaxisymmetric particle paths in this case.

Characterization of Swirling Flows in a Partly Open Cylinder

“…Above curves ( 2 ) and ( 3) the diagram exhibits a region of toroidal vortex partern over the approximate range 0.4 < ≤ 1 . It is worth mentioning that a vortex formation attached to the free surface is spontaneous and does not necessarily result from a migration process in accord with the statements reported in Hewitt et al (2008) who investigated a related problem of confined swirling flows driven by the corotation of co-axial disks.…”

“…These are based on the no slip conditions applied to solid walls and regularity assumption on the cavity axis. Reflexion symmetry is considered on the partly open surface, assumed flat stress-free, (Herrada et al 2014;Hewitt et al 2008;Saci et al 2008) over the range of the flow parameters considered. Initial conditions consider the fluid at rest and the bottom disk is impulsively rotated to a constant angular speed.…”

Free surface due to a flow driven by a rotating disk inside a vertical cylindrical tank: Axisymmetric configuration

“…Iwatsu 31 for G = 0.3 and Re = 1000 observed one cell attached to the free surface. Hewitt et al 32 observed experimentally, for the case of an enclosed co-rotating disks, several secondary cells attached to the horizontal mid-plane that could be assimilated to our free surface using an axial reflectional symmetry. Finally, Bouffanais and Lo Jacono 23 observed four cells for G = 1/3 and Re = 2000.…”

Nonlinear dynamo in a short Taylor–Couette setup

“…Abusing the notation, this immediately implies that R i = 1 and R o = 2 in nondimensional units. We did not explore other aspect ratios (see for example [14,1,11,9] for short aspect ratios and different angular velocities). The conducting domain Ω c is partitioned into its fluid part enclosed between the two walls, Ω cf , and its solid part enclosed in the inner cylinder, Ω cs .…”