Session F17: Vortex Turbulence and Superfluids

Vortex Interactions in Two-Dimensional Turbulence

Interactions of coherent vortices in decaying two-dimensional turbulence are quantitatively assessed.  Direct numerical simulations are performed, and a tracking algorithm is implemented to autonomously identify vortex structures and track their evolution in time.  Vortex properties such as circulation, area, vorticity, strain rate, and enstrophy are used to assess Individual interactions and their outcomes.  Inelastic interactions such as merging and straining out, observed here in a field of vortices, are compared with those characterized by isolated asymmetric vortex pairs (Folz and Nomura, JFM 2017).  The statistics of these interactions are interpreted in terms of their cumulative effects on the overall flow.   

What can two vortex tubes tell us about the turbulent cascade?

We numerically explore the violent interaction of two parallel, counter-rotating vortex tubes which causes the transfer of energy from the initial large, smooth tubes to the late-stage small ``worm''-like structures similar to those in Homogeneous Isotropic Turbulence simulations. Reynolds numbers of up to Re=Γ/ν=6000 are reached, where Γ is the is the vortex ring circulation, and ν the kinematic viscosity of the fluid. When the tubes are initially very close, their deformation is due to the elliptical instability. The tubes generate perpendicular filaments which undergo transformations of filaments into sheets into filaments, according to an iterative cascade of the type suggested by Brenner et al. (Phys. Rev. Flu., 1, 084503 (2016)). By numerically introducing different perturbations, we compare the dynamics resulting from the elliptical instability, to that induced by the Crow-like instabilities, which lead to reconnection. We show that the iterative mechanisms, triggered by the elliptical instability, transfers energy across scales much more efficiently as a whole than reconnection. We propose that this iterative mechanism is crucial for understanding the turbulent cascade.   

Vortex axis tracking by iterative propagation (VATIP): a method for analyzing three-dimensional turbulent structures

Study of turbulent vortices in DNS data relies heavily on direct visual inspection, anecdotal observations, and intuitive arguments. Quantitative analysis is limited by the lack of computational tools for the objective detection and extraction of vortex structures. Much progress has been made in the identification criteria of vortices, which, however, only label spatial regions belonging to vortices, without any information on the identity, topology, and shape of individual vortices. This latter information requires vortex tracking techniques and existing methods so far only focused on quasi-linear streamwise vortices. In this study, a new tracking algorithm is proposed which propagates along the vortex axis-lines and iteratively search for new directions for growth. It is the first tracking method designed for general three-dimensional vortices. The method is tested in transient flow fields with specific vortex types as well as DNS. A new procedure is also proposed that classifies vortices into commonly-observed shapes, including quasi-streamwise vortices, hairpins, hooks, and branches, based on their axis-line topology. The study offers a new tool-set for the fundamental study of the dynamics of turbulent coherent structures.   

Breakup and Reorganization of a Turbulent Batchelor Vortex

The breakup and reorganization, i.e. recombination of the vorticity filaments from the disrupted core into a columnar vortex due to pairing, merging and viscous diffusion, of a Batchelor vortex is studied using Smagorinsky model Large Eddy Simulation (LES). At Reynolds numbers (vortex circulation/viscosity) up to 500,000, an unstable Batchelor vortex embedded in random turbulence breaks up in to vorticity filaments. These filaments tend to form dipoles and advect away from the original axis due to the swirling jet flow. Regardless of the strength of the jet flow causing the instability, filaments near the core are nearly axial, and thus eventually undergo mutual rotation and eventually pair, merge and reorganize into a columnar structure. The effect of the core reorganization on vortex decay – decrease in the peak azimuthal velocity and increase in the radius of the peak azimuthal velocity – is discussed for the potential to model vortex evolution and predict the time to “safe” vortex states. Evolutions of the Oseen vortex embedded in turbulence as well as vortices excited with linear transient growth optimal perturbation eigenfunctions are compared to the Batchelor vortex cases to illustrate the changes to vortex evolution, breakup and reorganization with increasing axial flow.