Bifurcation of an elliptic vortex ring

Abstract

Time-dependent vorticity fields of elliptic vortex rings of aspect ratios 2, 3 and 4 were measured hy means of hot-wire anemornetry. The time evolution of their vorticity fields was analyzed and the processes of vortex ring formation, advection, interaction and decay, and the mechanism of vortex bifurcation arc studied. The following crosslinking model is proposed: A thick vortical region composed of many equivalent vortex filaments with distributed cores is initially formed at the orifice and they behave as inviscid filaments. The elliptic ring deforms and the end parts of its major axis get closer. Then. the vortex filaments interact at the touching point and the ring partially bifurcates. Almost simultaneously. turbulent spot appears at this point. and propagates around the ring cross section. thus preventing further bifurcation. And it becomes a turbulent blob, This model is also supported hy numerical simulation hy a high-order vortex method and the Navicr-i Stokes solution.

Evolution of single elliptic vortex rings

“…Oshima (1988)[5l predicted that the motion of a single elliptic vortex ring will bifurcate at AR .= 3.5, we find that the ring with AR --4 will reach a complicate middle state between periodic oscillation and complete splitting. Oshima (1988)[5l predicted that the motion of a single elliptic vortex ring will bifurcate at AR .= 3.5, we find that the ring with AR --4 will reach a complicate middle state between periodic oscillation and complete splitting.…”

Pinch-off of non-axisymmetric vortex rings

“…In particular, the behaviour of elliptical vortex rings is well documented in both computational (Arms & Hama 1965;Viets & Sforza 1972;Dhanak & de Bernardinis 1981;Fernandez, Zabusky & Gryanik 1995;Ryu & Lee 1997;Kimura 2006) and experimental studies (Oshima et al 1988;Hussain & Husain 1989;Hussain & Hussain 1991;Adhikari 2009). The bulk of these studies focused on the time-dependent deformation of the elliptical vortex ring due to the curvature dependence of the vortex propagation velocity (Arms & Hama 1965;Dhanak & de Bernardinis 1981;Viets & Sforza 1972).…”

Numerical investigation of the evolution of elliptic vortex ring

“…Arms and Hama (1965) studied the axis-switching periods of an elliptic vortex ring by the Localised-Induction Approximation method and proposed an expression to estimate the period as a function of the area and eccentricity of the ring. Oshima et al (1988) measured the time-dependent vorticity fields of elliptic vortex rings of aspect ratios 2, 3 and 4 using Hot-Wire Anemometry and studied the mechanism of vortex bifurcation. Zhao and Shi (1998) studied the evolution of single elliptic vortex rings of aspect ratios 2, 4 and 6 by solving the incompressible Navier-Stokes equations using a pseudo-spectral method and found that vortex rings with large aspect ratios will partially split into two new sub-rings.…”