On the self-similarity of line segments in decaying homogeneous isotropic turbulence

The self-similarity of a passive scalar in homogeneous isotropic decaying turbulence is investigated by the method of line segments (M. Gauding et al., Physics of Fluids 27.9 (2015): 095102). The analysis is based on a highly resolved direct numerical simulation of decaying turbulence. The method of line segments is used to perform a decomposition of the scalar field into smaller sub-units based on the extremal points of the scalar along a straight line. These sub-units (the so-called line segments) are parameterized by their length $\ell$ and the difference $\Delta\phi$ of the scalar field between the ending points. Line segments can be understood as thin local convective-diffusive structures in which diffusive processes are enhanced by compressive strain. From DNS, it is shown that the marginal distribution function of the length~$\ell$ assumes complete self-similarity when re-scaled by the mean length $\ell_m$. The joint statistics of $\Delta\phi$ and $\ell$, from which the local gradient $g=\Delta\phi/\ell$ can be defined, play an important role in understanding the turbulence mixing and flow structure. Large values of $g$ occur at a small but finite length scale. Statistics of $g$ are characterized by rare but strong deviations that exceed the standard deviation by more than one order of magnitude. It is shown that these events break complete self-similarity of line segments, which confirms the standard paradigm of turbulence that intense events (which are known as internal intermittency) are not self-similar

Lagrangian Structure Functions in Turbulence: A Quantitative Comparison between Experiment and Direct Numerical Simulation

A detailed comparison between data from experimental measurements and numerical simulations of Lagrangian velocity structure functions in turbulence is presented. By integrating information from experiments and numerics, a quantitative understanding of the velocity scaling properties over a wide range of time scales and Reynolds numbers is achieved. The local scaling properties of the Lagrangian velocity increments for the experimental and numerical data are in good quantitative agreement for all time lags. The degree of intermittency changes when measured close to the Kolmogorov time scales or at larger time lags. This study resolves apparent disagreements between experiment and numerics.Comment: 13 RevTeX pages (2 columns) + 8 figures include

On the Scales of Turbulent Motion at High Reynolds Numbers

Turbulence is a physical state of a fluid far from equilibrium. In turbulent flows, a huge number of degrees of freedom is excited and a wide range of interacting scales determines the flow characteristics. Turbulent flows are nonlinear and non-local. They exhibit chaotic spatial and temporal dynamics and extreme events are likely to occur. Up to today, there is no unified theory of turbulence, very few exact predictions from the governing equations are available and the precise predictability of the behavior of turbulent flows is limited. Additionally, it is not known exactly, how the flow quantities depend on the turbulent flow�s vigorousness that is given by the so-called Reynolds number. In this thesis, high-Reynolds number turbulence and its dependencies on the Reynolds number are investigated by the means of hot-wire measurements in the Variable Density Turbulence Tunnel at the Max-Planck-Institute for Dynamics and Self-Organization in G?ttingen. The Reynolds number dependence of the decay exponent of freely decaying turbulence is found to be consistent with Saffmans prediction. Furthermore, with extremely long datasets, the statistical properties of turbulence in the inertial range are investigated in great detail, finding deviations from the expected scaling behavior

Long Term Evolution of Magnetic Turbulence in Relativistic Collisionless Shocks: Electron-Positron Plasmas

We study the long term evolution of magnetic fields generated by a collisionless relativistic $e^+e^-$ shock which is initially unmagnetized. Our 2D particle-in-cell numerical simulations show that downstream of such a Weibel-mediated shock, particle distributions are close to isotropic, relativistic Maxwellians, and the magnetic turbulence is highly intermittent spatially, with the non-propagating magnetic fields forming relatively isolated regions with transverse dimension $\sim 10-20$ skin depths. These structures decay in amplitude, with little sign of downstream merging. The fields start with magnetic energy density $\sim (0.1-0.2)$ of the upstream kinetic energy within the shock transition, but rapid downstream decay drives the fields to much smaller values, below $10^{-3}$ of equipartition after $10^3$ skin depths. In an attempt to construct a theory that follows field decay to these smaller values, we explore the hypothesis that the observed damping is a variant of Landau damping in an unmagnetized plasma. The model is based on the small value of the downstream magnetic energy density, which suggests that particle orbits are only weakly perturbed from straight line motion, if the turbulence is homogeneous. Using linear kinetic theory applied to electromagnetic fields in an isotropic, relativistic Maxwellian plasma, we find a simple analytic form for the damping rates, $\gamma_k$, in two and three dimensions for small amplitude, subluminous electromagnetic fields. We find that magnetic energy does damp due to phase mixing of current carrying particles as $(\omega_p t)^{-q}$ with $q \sim 1$. (abridged)Comment: 10 pages, 6 figures, accepted to ApJ; Downsampled version for arXiv. Full resolution figures available at http://astro.berkeley.edu/~pchang/full_res_weibel.pd

Astrophysical turbulence modeling

The role of turbulence in various astrophysical settings is reviewed. Among the differences to laboratory and atmospheric turbulence we highlight the ubiquitous presence of magnetic fields that are generally produced and maintained by dynamo action. The extreme temperature and density contrasts and stratifications are emphasized in connection with turbulence in the interstellar medium and in stars with outer convection zones, respectively. In many cases turbulence plays an essential role in facilitating enhanced transport of mass, momentum, energy, and magnetic fields in terms of the corresponding coarse-grained mean fields. Those transport properties are usually strongly modified by anisotropies and often completely new effects emerge in such a description that have no correspondence in terms of the original (non coarse-grained) fields.Comment: 88 pages, 26 figures, published in Reports on Progress in Physic