Passive directors in turbulence

Abstract

In experiments and numerical simulations we measured angles between the symmetry axes of small spheroids advected in turbulence (passive directors). Since turbulent strains tend to align nearby spheroids, one might think that their relative angles are quite small. We show that this intuition fails in general because angles between the symmetry axes of nearby particles are anomalously large. We identify two mechanisms that cause this phenomenon. First, the dynamics evolves to a fractal attractor despite the fact that the fluid velocity is spatially smooth at small scales. Second, this fractal forms steps akin to scar lines observed in the director patterns for random or chaotic two-dimensional maps. arXiv:1707.06037v3 [physics.flu-dyn]

Alignment statistics of rods with the Lagrangian stretching direction in a channel flow

“…In order to make progress, in the rest of this section we use a statistical model for the fluid-velocity gradients. In our statistical model we assume that the fluctuations of fluid velocity-gradients are much quicker than the time scale associated with the angular dynamics of rods (Zhao et al 2019). Such statistical models have led to important insights in the dynamics of small spherical particles in turbulence (Gustavsson et al 2016), as well as dynamics of relative angles between rods in turbulence (Zhao et al 2019).…”

“…In our statistical model we assume that the fluctuations of fluid velocity-gradients are much quicker than the time scale associated with the angular dynamics of rods (Zhao et al 2019). Such statistical models have led to important insights in the dynamics of small spherical particles in turbulence (Gustavsson et al 2016), as well as dynamics of relative angles between rods in turbulence (Zhao et al 2019). The flow near the centre of a turbulent channel flow resembles homogeneous, isotropic turbulence, where the time scales of angular dynamics of rods and fluctuations of fluid velocity-gradients are in fact very similar (Pumir & Wilkinson 2011).…”

“…To qualitatively explain why the distributions in figure 3 have power-law tails we consider a two-dimensional toy model for the angular dynamics (Zhao et al 2019). In two dimensions, the left Cauchy–Green tensor has two eigenvectors, the expanding eigenvector and the contracting eigenvector , but not the intermediate eigenvector .…”

“…The angular dynamics of small non-spherical particles advected in turbulence and other mixing flows is a subject of significant recent interest (Wilkinson, Bezuglyy & Mehlig 2009; Parsa et al 2012; Chevillard & Meneveau 2013; Gustavsson, Einarsson & Mehlig 2014; Ni, Ouelette & Voth 2014; Byron et al 2015; Zhao et al 2015; Einarsson et al 2016; Hejazi, Mehlig & Voth 2017; Voth & Soldati 2017; Zhao et al 2019). In these studies it is assumed that the particles are small enough so that inertial effects can be neglected (Subramanian & Koch 2005; Einarsson, Angilella & Mehlig 2014; Einarsson et al 2015; Rosén et al 2015), but the particles are large enough to neglect rotational diffusion (Hinch & Leal 1972).…”

“…The models assume that the fluid-velocity gradients experienced by the tracer rod fluctuate rapidly (Gustavsson et al 2016). This white-noise limit has also proved useful in understanding the dynamics of relative separations of spherical particles in turbulence (see Gustavsson et al (2016) for a review) and has been used to study relative angles between nearby rods in turbulence (Zhao et al 2019). In turbulence, near the channel centre, the fluid-velocity gradients fluctuate on the same time scale as the angular dynamics of slender rods.…”