On the characteristics of vortex filaments in isotropic turbulence

Abstract

The statistical properties of the strong coherent vortices observed in numerical simulations of isotropic turbulence are studied. When compiled at axial vorticity levels ω/ω′∼Re1/2λ, where ω′ is the r.m.s. vorticity magnitude for the flow as a whole, they have radii of the order of the Kolmogorov scale and internal velocity differences of the order of the r.m.s. velocity of the flow u′. Theoretical arguments are given to explain these scalings. It is shown that the filaments are inhomogeneous Burgers' vortices driven by an axial stretching which behaves like the strain fluctuations of the background flow. It is suggested that they are the strongest members in a class of coherent objects, the weakest of which have radii of the order of the Taylor microscale, and indirect evidence is presented that they are unstable. A model is proposed in which this instability leads to a cascade of coherent filaments whose radii are below the dissipative scale of the flow as a whole. A family of such cascades separates the self-similar inertial range from the dissipative limit. At the vorticity level given above, the filaments occupy a volume fraction which scales as Re−2λ, and their total length increases as O(Reλ). The length of individual filaments scales as the integral length of the flow, but there is a shorter internal length of the order of the Taylor microscale.

Coherent structures in statistically stationary homogeneous shear turbulence

“…The inner dimension of vortex clusters in figure 6(d) is r 1 ≈ 6η, independently of the cluster volume, which approximately agrees with the diameter of individual filamentary vortices in turbulence (Jiménez & Wray 1998;Tanahashi, Iwase & Miyauchi 2001;del Álamo et al 2006;Pirozzoli, Bernardini & Grasso 2008;Stanislas, Perret & Foucaut 2008). It is also consistent with the description of vortex clusters as 'sponges of strings' (LFJ12).…”

Interfaces and inhomogeneous turbulence

“…This is because these vortices are undergoing significant distortion [14] and are unlike equilibrium Burgers vortices which have been proposed as a generic model (e.g. [26]). The intense small-scale velocity fluctuations induced by the vortices are probably associated with the small-scale 'nibbling process' that determines the boundary entrainment velocity, E b [27].…”

Vorticity filaments beneath regular turbulent flow

“…They observed that at the beginning of the merging, two strong filaments of vorticity are ejected, and roll up around the final vortex due to the differential rotation, leading to an axisymmetric vortex at late stages. Just as in previous work by Kevlahan and Farge (1997), Elhmaidi et al (2004), Dritschel (1989), Jimenez et al (1993), Jimenez and Wray (1998), Meunier et al (2005) and Petitjeans (2003), narrow strips of intense vorticity are what is meant when referring to 'vorticity filaments' in this work. However, as pointed out by (Petitjeans 2003), the presence of vorticity does not imply the existence of a vortex, e.g.…”

“…The same objects have been identified by locating local minima of pressure fields in numerical experiments (Belin et al 1996). Dritschel et al (1991) noted that a common feature of strongly non-linear, high Reynolds number, two-dimensional flows is the presence of thin filaments of vorticity, while Jimenez and Wray (1998) also observed that most of the strong vorticity in the flow field is in the form of filaments. According to Elhmaidi et al (2004), vorticity filaments are easily generated during vortex-vortex interactions (such as vortex merger), and when vortices are exposed to strong shearing.…”

“…Simulations by Jimenez and Wray (1998) have shown that the filaments can simultaneously have lengths of the order of the injection scale and a core diameter as small as the Kolmogorov scale. A pair of counter-rotating filaments has an estimated centre separation of about 2.0 cm.…”