Persistent accelerations disentangle Lagrangian turbulence

Abstract

Particles in turbulence frequently encounter extreme accelerations between extended periods of quiescence. The occurrence of extreme events is closely related to the intermittent spatial distribution of intense flow structures such as vorticity filaments. This mixed history of flow conditions leads to very complex particle statistics with a pronounced scale dependence, which presents one of the major challenges on the way to a non-equilibrium statistical mechanics of turbulence. Here, we introduce the notion of persistent Lagrangian acceleration, quantified by the squared particle acceleration coarse-grained over a viscous time scale. Conditioning Lagrangian particle data from simulations on this coarse-grained acceleration, we find remarkably simple, close-to-Gaussian statistics for a range of Reynolds numbers. This opens the possibility to decompose the complex particle statistics into much simpler sub-ensembles. Based on this observation, we develop a comprehensive theoretical framework for Lagrangian single-particle statistics that captures the acceleration, velocity increments as well as single-particle dispersion.

On small-scale and large-scale intermittency of Lagrangian statistics in canopy flow

“…Let us briefly consider dynamical scenarios for small-scale Lagrangian intermittency. Results from HIT DNS by Biferale et al (2005), Bec et al (2006) and Bentkamp et al (2019) suggested that small-scale intermittency is a result of encounters between particles and intense vortex filaments; indeed, Wilczek, Jenko & Friedrich (2008) showed that the characteristic transition of the increments' p.d.f.s can be captured by a heuristic flow model of superimposed constitutive vortices. Similarly, Liberzon et al (2012) showed that acceleration-vorticity-strain alignment in a quasi-homogeneous flow is associated with intense energy flux.…”

“…2019) and proposed modelling strategies (Wilczek et al. 2013; Bentkamp, Lalescu & Wilczek 2019). These works focused on homogeneous isotropic turbulent flows and, inevitably so, focused on small-scale intermittency.…”

“…Intermittency in turbulence was studied previously mostly in the Eulerian framework, yet the advent of technological advances of the 2000s enabled empirical investigations in the Lagrangian framework as well (as reviewed by Toschi & Bodenschatz (2009)). Previous Lagrangian studies have revealed the existence of anomalous scaling of velocity differences (Chevillard et al 2003;Arnèodo et al 2008;Benzi et al 2010;Huang et al 2013) and has examined local flow features associated with extreme events (Liberzon et al 2012;Xu et al 2014;Watteaux et al 2019) and proposed modelling strategies (Wilczek et al 2013;Bentkamp, Lalescu & Wilczek 2019). These works focused on homogeneous isotropic turbulent flows and, inevitably so, focused on small-scale intermittency.…”

Modelling Lagrangian velocity and acceleration in turbulent flows as infinitely differentiable stochastic processes

“…This random field is Gaussian, zero average and taken independent of the white noise instance W(dt), and is thus fully characterized by its correlation function. To reproduce intermittent corrections, as they have been observed in Lagrangian turbulence (see Yeung & Pope 1989;Voth et al 1998;La Porta et al 2001;Mordant et al 2001Mordant et al , 2002Mordant et al , 2003Chevillard et al 2003;Biferale et al 2004;Toschi & Bodenschatz 2009;Pinton & Sawford 2012;Bentkamp et al 2019, and references therein), we demand the Gaussian field X 1, to be logarithmically correlated (Bacry et al 2001). Such a correlation structure implies in particular that the variance of X 1, diverges as → 0, making it difficult to give a proper mathematical meaning to such a field.…”

“…As mentioned, since its dynamics is made of embedded linear operations on a Gaussian white noise, it is itself Gaussian. Such a Gaussian framework, in particular for acceleration, is at odds with experimental and numerical investigations of Lagrangian turbulence (see Yeung & Pope 1989; Voth, Satyanarayan & Bodenschatz 1998; La Porta et al 2001; Mordant et al 2001, 2002, 2003; Chevillard et al 2003; Friedrich 2003; Biferale et al 2004; Toschi & Bodenschatz 2009; Pinton & Sawford 2012; Bentkamp, Lalescu & Wilczek 2019, and references therein). As correctly predicted by Borgas (1993), the observed level of intermittency in the Lagrangian framework is found much higher than in the Eulerian framework (Frisch 1995).…”