The evolution of a perturbed vortex in a pipe to axisymmetric vortex breakdown

• Published in: Journal of fluid mechanics Vol. 366; pp. 211 - 237
• Main Authors: RUSAK, Z., WANG, S., WHITING, C. H.
• Format: Journal Article
• Language: English
• Published: Cambridge Cambridge University Press 10.07.1998
• Subjects: Exact sciences and technology; Flows in ducts, channels, nozzles, and conduits; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydrodynamic stability; Inviscid instability; Physics; Rotational flow and vorticity; Vortex dynamics; Pipe flow; Non viscous fluid; Digital simulation; Vortices; Bifurcation; Theoretical study; Bursting; Vortex flow; Burgers equation; Axial symmetry
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112098001396

The evolution of a perturbed vortex in a pipe to axisymmetric vortex breakdown is studied through numerical computations. These unique simulations are guided by a recent rigorous theory on this subject presented by Wang & Rusak (1997a). Using the unsteady and axisymmetric Euler equations, the nonlinear dynamics of both small- and large-amplitude disturbances in a swirling flow are described and the transition to axisymmetric breakdown is demonstrated. The simulations clarify the relation between our linear stability analyses of swirling flows (Wang & Rusak 1996a, b) and the time-asymptotic behaviour of the flow as described by steady-state solutions of the problem presented in Wang & Rusak (1997a). The numerical calculations support the theoretical predictions and shed light on the mechanism leading to the breakdown process in swirling flows. It has also been demonstrated that the fundamental characteristics which lead to vortex instability and breakdown in high-Reynolds-number flows may be calculated from considerations of a single, reduced-order, nonlinear ordinary differential equation, representing a columnar flow problem. Necessary and sufficient criteria for the onset of vortex breakdown in a Burgers vortex are presented.