Intermittency in the relative separations of tracers and of heavy particles in turbulent flows
L. Biferale,  A.S. Lanotte, R. Scatamacchia and F. Toschi
Journ. Fluid Mech 757, 550 (2014) arXiv:
Abstract: Results from direct numerical simulations (DNS) of particle relative dispersion
in three-dimensional homogeneous and isotropic turbulence at Reynolds number
Re 300 a re presented. We study point-like passive tracers and heavy particles,
at Stokes number St  0.6, 1.0 and 5. Particles are emitted from localised sources,
in bunches of thousands, periodically in time, allowing an unprecedented statistical
accuracy to be reached, with a total number of events for two-point observables
of the order of 10^11. The right tail of the probability density function (PDF) for
tracers develops a clear deviation from Richardson’s self-similar prediction, pointing
to the intermittent nature of the dispersion process. In our numerical experiment,
such deviations are manifest once the probability to measure an event becomes of the
order of – or rarer than – one part over one million, hence the crucial importance of
a large dataset. The role of finite-Reynolds-number effects and the related fluctuations
when pair separations cross the boundary between viscous and inertial range scales are
discussed. An asymptotic prediction based on the multifractal theory for inertial range
intermittency and valid for large Reynolds numbers is found to agree with the data
better than the Richardson theory. The agreement is improved when considering heavy
particles, whose inertia filters out viscous scale fluctuations. By using the exit-time
statistics we also show that events associated with pairs experiencing unusually slow
inertial range separations have a non-self-similar PDF.

Pair separation of magnetic elements in the quiet Sun
F. Giannattasio, F. Berrilli, L. Biferale, D. Del Moro, M. Sbragaglia, L. Bellot Rubio, M. Go˘si´c, D. Orozco
Suárez
Astronomy & Astrophysics 569, A121  (2014). DOI: 10.1051/0004-6361/201424380. arXiv:1409.1010
Abstract: The dynamic properties of the quiet Sun photosphere can be investigated by analyzing the pair dispersion of small-scale magnetic fields (i.e.,magnetic elements). By using 25 h-long Hinode magnetograms at high spatial resolution (0. 3), we tracked 68 490 magnetic element pairs within a supergranular cell near the disk center. The computed pair separation spectrum, calculated on the whole set of particle pairs independently of their initial separation, points out what is known as a super-diffusive regime with spectral index
γ = 1.55 ± 0.05, in agreement with the most recent literature, but extended to unprecedented spatial and temporal scales (from
granular to supergranular). Furthermore, for the first time, we investigated here the spectrum of the mean square displacement of pairs
of magnetic elements, depending on their initial separation r0.We found that there is a typical initial distance above (below) which the
pair separation is faster (slower) than the average. A possible physical interpretation of such a typical spatial scale is also provided.


Deformation statistics of sub-Kolmogorov-scale ellipsoidal drops in isotropic turbulence
L. Biferale, C. Meneveau and R. Verzicco
J. Fluid Mech. 754 184-207 (2014).  arXiv:1409.0918
Abstract:Small droplets in turbulent flows can undergo highly variable deformations and orientational dynamics. For neutrally buoyant droplets smaller than the Kolmogorov scale, the dominant effects from the surrounding turbulent flow arise through Lagrangian time histories of the velocity gradient tensor. Here we study the evolution of representative droplets using a model that includes rotation and stretching effects
from the surrounding fluid, and restoration effects from surface tension including a constant droplet volume constraint, while assuming that the droplets maintain an ellipsoidal shape. The model is combined with Lagrangian time histories of the velocity gradient tensor extracted from direct numerical simulations (DNS) of turbulence to obtain simulated droplet evolutions. These are used to characterize the size, shape and orientation statistics of small droplets in turbulence. A critical capillary number is identified associated with unbounded growth of one or two of the droplet’s semi-axes. Exploiting analogies with dynamics of polymers in turbulence, the critical capillary number can be predicted based on the large deviation theory for the largest finite-time Lyapunov exponent quantifying the chaotic separation of particle trajectories. Also, for subcritical capillary numbers near the critical value, the theory enables predictions of the slope of the power-law tails of droplet size distributions in turbulence. For cases when the viscosities of droplet and outer fluid differ in a way that enables vorticity to decorrelate the shape from the straining directions, the large deviation formalism based on the stretching properties of the velocity gradient tensor loses validity and its predictions fail. Even considering the limitations of the assumed ellipsoidal droplet shape, the results highlight the complex coupling between droplet deformation, orientation and the local fluid velocity gradient tensor to be expected when small viscous drops interact with turbulent flows. The results also underscore the usefulness of large deviation theory to model these highly complex couplings and fluctuations in turbulence that result from time integrated effects of fluid deformations.

Evolution of a double-front Rayleigh-Taylor system using a GPU-based high resolution thermal Lattice-Boltzmann model
P. Ripesi, L. Biferale, S.F. Schifano and R. Tripiccione
Phys. Rev. E 89 043022 (2014). arXiv:1405.1253
Abstract: We study the turbulent evolution originated from a system subjected to a Rayleigh-Taylor instability with a double density at high resolution in a 2 dimensional geometry using a highly optimized thermal Lattice Boltzmann code for GPUs. The novelty of our investigation stems from the initial condition, given by the superposition of three layers with three different densities, leading to the development of two Rayleigh-Taylor fronts that expand upward and downward and collide in the middle of the cell. By using high resolution numerical data we highlight the effects induced by the collision of the two turbulent fronts in the long time asymptotic regime. We also provide details on the optimized Lattice-Boltzmann code that we have run on a cluster of GPUs