Dynamics of thin vortex rings

Abstract

As part of a long-range study of vortex rings, their dynamics, interactions with boundaries and with each other, we present the results of experiments on thin core rings generated by a piston gun in water. We characterize the dynamics of these rings by means of the traditional equations for such rings in an inviscid fluid suitably modifying them to be applicable to a viscous fluid. We develop expressions for the radius, core size, circulation and bubble dimensions of these rings. We report the direct measurement of the impulse of a vortex ring by means of a physical pendulum.

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

“…At t = 8, shown in figure 6(l), secondary vortical structures are formed around the original vortex core apart from the finger-like structures outside the core. These secondary structures have previously been termed as 'halo' vorticity and were also observed in previous DNS and experimental works (Bergdorf et al 2007;Archer et al 2008;Sullivan et al 2008). The finger-like structures are outcomes of the optimal transient energy growth, and their forms are similar to the well reported lobe structures, which however are located in the vortex core (Shadden, Dabiri & Marsden 2006).…”

“…From the outcome of the corresponding optimal initial perturbations (not shown here), these optimal growths are associated with the core of the ring and dominated by the elliptic instability induced by the elliptic streamlines of the base flow in the core region (Kerswell 2002;Blanco-Rodríguez & Le Dizèz 2016a,b). The wavenumber of the elliptic unstable modes has been found to vary according to the Transient growth on a vortex ring and its transition via cascade of ringlets ring's slenderness ratio (core/ring radius) and Re, and 8-10 azimuthal standing waves have been observed in previous DNSs and experiments (Archer et al 2008;Sullivan et al 2008). Over short times, e.g.…”

Modelling of confined vortex rings

“…Laminar vortex rings are usually produced in laboratories by pushing a column of fluid (by a piston/cylinder mechanism, e. g. Gharib et al (1998), or a piston gun, e. g. Sullivan et al (2008)) through a long pipe of diameter D. In what follows, all parameters are normalised using D as the length-scale and the maximum piston velocity U 0 as the velocity scale. The main physical parameter of the flow is the Reynolds number based on the pipe diameter:…”

A multipole-expanded effective field theory for vortex ring-sound interactions

“…At zero temperature, which is what we will assume here, the conditions above are enough to determine the low-energy dynamics of the system. 3 The condition of having a finite density is usually implemented by introducing a chemical potentialμ and demanding that the equilibrium state |ψ be the ground state of the modified Hamiltonian [13] …”