ausblenden:
Schlagwörter:
Physics, Fluid Dynamics, physics.flu-dyn,Nonlinear Sciences, Chaotic Dynamics, nlin.CD
Zusammenfassung:
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.
