2 research outputs found
Persistent accelerations disentangle Lagrangian turbulence
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
The statistical geometry of material loops in turbulence
Material elements - which are lines, surfaces, or volumes behaving as
passive, non-diffusive markers of dye - provide an inherently geometric window
into the intricate dynamics of chaotic flows. Their stretching and folding
dynamics has immediate implications for mixing in the oceans or the atmosphere,
as well as the emergence of self-sustained dynamos in astrophysical settings.
Here, we uncover robust statistical properties of an ensemble of material loops
in a turbulent environment. Our approach combines high-resolution direct
numerical simulations of Navier-Stokes turbulence, stochastic models, and
dynamical systems techniques to reveal predictable, universal features of these
complex objects. We show that the loop curvature statistics become stationary
through a dynamical formation process of high-curvature slings, leading to
distributions with power-law tails whose exponents are determined by the
large-deviations statistics of finite-time Lyapunov exponents of the background
flow. This prediction applies to advected material lines in a broad range of
chaotic flows. To complement this dynamical picture, we confirm our theory in
the analytically tractable Kraichnan model with an exact Fokker-Planck
approach