Optimal transient growth on a vortex ring and its transition via cascade of ringlets

Abstract

Linear and nonlinear transient growths of perturbations on a vortex ring up to Reynolds number (≡ circulation/viscosity) Re = 27 000 are studied. For short time intervals, perturbations around the ring axis undergo the strongest linear transient growth and lead to secondary structures in the form of ringlets, owing to the Orr mechanism and an inviscid vorticity-amplification mechanism: in contrast to the well-reported instabilities and lobe structures along the vortex ring core. These secondary ringlet structures induce a tertiary group of ringlets through similar transient perturbation growth. This cascade of ringlets lead to the breakup of the main ring even before activation of the vortex-core instabilities. Such a cascade scenario is also observed in the development of a vortex ring perturbed by random disturbance in the axis region. These new modes and mechanisms for the generation and breakup of vortex ring structures bring insights into the dynamics and control of vortex ring flows.

A physical model of turbulence cascade via vortex reconnection sequence and avalanche

“…From the spectral perspective, the energy cascade is understood as the interaction between adjacent wavenumbers (Obukhov 1941;Domaradzki & Carati 2007). From the spatial perspective, energy transfer across different scales is often assumed to be due to vortex stretching, in which vortical structures of a given scale are stretched and intensified by larger vortices (Taylor & Green 1937;Goto 2008;Mao & Hussain 2017;Doan et al 2018). However, the link between these two approaches is still unclear.…”

Collision of vortex rings upon V-walls

“…It should come as no surprise then, that significant research has been expended to expand our fundamental understanding of vortex rings and how they interact with their surroundings. Take, for instance, more recent studies on the behaviour of translating discrete circular vortex rings that would include Maxworthy (1972), Didden (1979), Pullin (1979), Glezer (1988), Glezer & Coles (1990), Nitsche & Krasny (1994), Heeg & Riley (1997), Gharib, Rambod & Shariff (1998), Mohseni & Gharib (1998), Mohseni, Ran& Colonius (2001), Krueger, Paul & Gharib (2003), Krueger, Dabiri & Gharib (2006), Shusser et al (2006), Feng, Kaganovskiy & Krasny (2009), Kaplanski et al (2009), Gao & Yu (2010), Gan, Dawson & Nickels (2012), Ponitz, Sastuba & Brücker (2016) and Mao & Hussain (2017), among many others. These investigations primarily focused upon how initial and boundary conditions affect vortex-ring generation, nature of laminar and turbulent vortex-ring formation and propagation, vortex-ring formation time scales, azimuthal wave instabilities, relationships between the initial vortex rings in starting jets, and other important characteristics.…”

Numerical stability analysis of a vortex ring with swirl

“…Numerical results have revealed some features of the elliptic instability; a map of unstable modes has been obtained recently by Gargan-Shingles, Rudman & Ryan (2016) for vortex rings with swirl, where swirl implies the azimuthal or toroidal component of velocity in the present paper. See also Mao & Hussain (2017) for transient growth and Shari↵, Verzicco & Orlandi (1994) for an early pioneering work. However, clear evidence of the curvature instability has not been observed in experiments or numerical simulations as far as the authors know.…”