Cascade leading to the emergence of small structures in vortex ring collisions

Abstract

When vortex rings collide head-on at high enough Reynolds numbers, they ultimately annihilate through a violent interaction which breaks down their cores into a turbulent cloud. We experimentally show that this very strong interaction, which leads to the production of fluid motion at very fine scales, uncovers direct evidence of a novel iterative cascade of instabilities in a bulk fluid. When the coherent vortex cores approach each other, they deform into tent-like structures, and the mutual strain causes them to locally flatten into extremely thin vortex sheets. These sheets then break down into smaller secondary vortex filaments, which themselves rapidly flatten and break down into even smaller tertiary filaments. By performing numerical simulations of the full Navier-Stokes equations, we also resolve one iteration of this instability and highlight the subtle role that viscosity must play in the rupturing of a vortex sheet. The concurrence of this observed iterative cascade of instabilities over various scales with those of recent theoretical predictions could provide a new mechanistic framework in which the evolution of turbulent flows can be examined in real-time as a series of discrete dynamic instabilities. arXiv:1802.09973v3 [physics.flu-dyn]

A filamentary cascade model of the inertial range

“…This is somewhat reminiscent of "rings on rings", but quite different from the splitting of thin helices which we invoke here. Nevertheless the structure we propose does bear some resemblance to shredding of unstable vortices seen by McKeown et al [7] The physical structure considered here can reproduce with remarkable accuracy the She-Leveque expression for ζ p . For example, with λ 0 = λ 1 and β 0 = 0.4376 the ratio of the two expressions varies from 0.9954 to 1.0037 for p to 10.…”

“…An alternative to the helix could be a configuration of rings encircling the par-ent filament. The rings might alternate in orientation, which is close to the structures observed in [7,8], see [4]. Other windings which conserve helicity are possible.…”

Towards a finite-time singularity of the Navier–Stokes equations. Part 2. Vortex reconnection and singularity evasion

“…The above neglect of core deformation calls for comment. There is evidence from DNS, such as in the recent investigations of McKeown et al (2018) and Kerr (2018) and in earlier studies, that there is a flattening of the vortex cores during the interaction process when δ/s increases to O(1). We have argued in MK19 that this flattening should decrease with increasing Reynolds number, on the grounds that the vortices are then spinning so rapidly that they experience an effectively axisymmetric strain near the tipping points.…”

Structure, dynamics, and reconnection of vortices in a nonlocal model of superfluids

“…The statistical analysis of the kinematic quantities involved in the dynamics, in particular current j and pseudo-vorticity w = ∇ ∧ j, shows that there is no creation of scales smaller that the injected atomic length size a. This makes a big difference with what is ob-tained with the incompressible Euler or Navier-Stokes equations, where a cascading phenomenon transfers energy towards the small scales, as recently put in evidence while considering two colliding vortex rings in a experimental (classical) flow [58]. We can thus infer that the hydrodynamics implied by the local and non-local versions of the GP equations, because of its implied high level of compressibility in the vicinity of the vortices, and the unclear action of the additional quantum pressure term, is indeed very different from the one of incompressible viscous Newtonian fluids.…”