Multiple helical modes of vortex breakdown

Abstract

Experimental observations of vortex breakdown in a rotating lid-driven cavity are presented. The results show that vortex breakdown for cavities with high aspect ratios is associated with the appearance of stable helical vortex multiplets. By using results from stability theory generalizing Kelvin's problem on vortex polygon stability, and systematically exploring the cavity flow, we succeeded in identifying two new stable vortex breakdown states consisting of triple and quadruple helical multiplets.

A flow in the depth of infinite annular cylindrical cavity

“…As Re exceeds its critical value, Re cr , typically a few thousands, the flow instability results in unsteady and threedimensional motion. Experiments (Sorensen et al 2011) and simulations (Lopez 2012) indicate that Re cr increases roughly proportionally to the aspect ratio in elongated containers. Therefore the asymptotic steady axisymmetric flow, as the aspect ratio tends to infinity, merits study.…”

“…Even if boundary conditions are steady and axisymmetric, a flow can be time-dependent and three-dimensional due to instability, as has been shown for the container with a rotating end wall (Sorensen, Naumov & Okulov 2011;Lopez 2012). Any ZRF flow decays as the distance from the flow source increases, and eventually becomes so slow that it can be governed by the linear Stokes equations rather than the nonlinear Navier-Stokes equations.…”

A study of the geometry and parameter dependence of vortex breakdown

“…The onset of precession of the breakdown bubbles in the TDC has, however, been observed for high Reynolds numbers 36,37 and at cylinder aspect ratios above 3.3, asymmetry has also been observed. 38,39 The different observations of breakdown in the low Reynolds number confined flows, and the high Reynolds number open flows, have caused some to question the relationship between the breakdowns observed in these different situations. Importantly, although there may be some degree of implicit understanding of the relationship between different breakdown states by experienced workers in the field, to the authors' knowledge, few papers have specifically addressed the reasons for the different manifestations.…”

The effect of a uniform magnetic field on vortex breakdown in a cylinder with rotating upper lid

“…Cogan et al [17] did a similar numerical study in open cylinders of rotating base, and indicated that the primary instability which leads to transition from steady axisymmetric flow to unsteady three-dimensional flow is related to the deformation of shear layers. In recent years, some special topics in cylindrical enclosure systems, e.g., the control of vortex breakdown [18], the rotating end wall of varied velocity [19] and helical vortex breakdown [20], have already attracted the researchers' interesting.…”