Fluctuation dynamo amplified by intermittent shear bursts in convectively driven magnetohydrodynamic turbulence

Intermittent large-scale high-shear flows are found to occur frequently and spontaneously in direct numerical simulations of statistically stationary turbulent Boussinesq magnetohydrodynamic (MHD) convection. The energetic steady-state of the system is sustained by convective driving of the velocity field and small-scale dynamo action. The intermittent emergence of flow structures with strong velocity and magnetic shearing generates magnetic energy at an elevated rate over time-scales longer than the characteristic time of the large-scale convective motion. The resilience of magnetic energy amplification suggests that intermittent shear-bursts are a significant driver of dynamo action in turbulent magnetoconvection

Extreme-value statistics from Lagrangian convex hull analysis for homogeneous turbulent Boussinesq convection and MHD convection

We investigate the utility of the convex hull of many Lagrangian tracers to analyze transport properties of turbulent flows with different anisotropy. In direct numerical simulations of statistically homogeneous and stationary Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD Boussinesq convection a comparison with Lagrangian pair dispersion shows that convex hull statistics capture the asymptotic dispersive behavior of a large group of passive tracer particles. Moreover, convex hull analysis provides additional information on the sub-ensemble of tracers that on average disperse most efficiently in the form of extreme value statistics and flow anisotropy via the geometric properties of the convex hulls. We use the convex hull surface geometry to examine the anisotropy that occurs in turbulent convection. Applying extreme value theory, we show that the maximal square extensions of convex hull vertices are well described by a classic extreme value distribution, the Gumbel distribution. During turbulent convection, intermittent convective plumes grow and accelerate the dispersion of Lagrangian tracers. Convex hull analysis yields information that supplements standard Lagrangian analysis of coherent turbulent structures and their influence on the global statistics of the flow.Comment: 18 pages, 10 figures, preprin

Diffusion and dispersion of passive tracers: Navier-Stokes versus MHD turbulence

A comparison of turbulent diffusion and pair-dispersion in homogeneous, macroscopically isotropic Navier-Stokes (NS) and nonhelical magnetohydrodynamic (MHD) turbulence based on high-resolution direct numerical simulations is presented. Significant differences between MHD and NS systems are observed in the pair-dispersion properties, in particular a strong reduction of the separation velocity in MHD turbulence as compared to the NS case. It is shown that in MHD turbulence the average pair-dispersion is slowed down for $\tau_\mathrm{d}\lesssim t\lesssim 10 \tau_\mathrm{d}$, $\tau_\mathrm{d}$ being the Kolmogorov time, due to the alignment of the relative Lagrangian tracer velocity with the local magnetic field. Significant differences in turbulent single-particle diffusion in NS and MHD turbulence are not detected. The fluid particle trajectories in the vicinity of the smallest dissipative structures are found to be characterisically different although these comparably rare events have a negligible influence on the statistics investigated in this work.Comment: Europhysics Letters, in prin

Method of Manufacture of Multiple-Element Piezoelectric Transducer

An improved method for fabrication of a multiple-element piezoelectric transducer and the transducer produced thereby. A green precursor tape is produced by doctor-blade tape-casting of a slurry containing lead zirconate-titanate (PZT) powder. After drying, individual strips of the tape are stacked between flat plates of previously sintered PZT, and sintered to form PZT strips; Pb from the previously sintered PZT plates makes up any Pb lost from the surfaces of the tape strips during sintering. The PZT strips are stacked interposed by layers of a thermoplastic polymer, and heated to a temperature above the melting point of the polymer, forming a laminate block. This block is then sliced perpendicular to the plane of the layers, forming slabs of alternate PZT and polymer layers; the slabs are then sliced perpendicular to the first slicing planes, forming strips of alternating PZT and polymer material. Electrodes are then added to complete the transducer assembly

Scaling properties of granular materials

Given an assembly of viscoelastic spheres with certain material properties, we raise the question how the macroscopic properties of the assembly will change if all lengths of the system, i.e. radii, container size etc., are scaled by a constant. The result leads to a method to scale down experiments to lab-size.Comment: 4 pages, 2 figure

Nonlinear Competition Between Small and Large Hexagonal Patterns

Recent experiments by Kudrolli, Pier and Gollub on surface waves, parametrically excited by two-frequency forcing, show a transition from a small hexagonal standing wave pattern to a triangular ``superlattice'' pattern. We show that generically the hexagons and the superlattice wave patterns bifurcate simultaneously from the flat surface state as the forcing amplitude is increased, and that the experimentally-observed transition can be described by considering a low-dimensional bifurcation problem. A number of predictions come out of this general analysis.Comment: 4 pages, RevTex, revised, to appear in Phys. Rev. Let

Stripe-hexagon competition in forced pattern forming systems with broken up-down symmetry

We investigate the response of two-dimensional pattern forming systems with a broken up-down symmetry, such as chemical reactions, to spatially resonant forcing and propose related experiments. The nonlinear behavior immediately above threshold is analyzed in terms of amplitude equations suggested for a $1:2$ and $1:1$ ratio between the wavelength of the spatial periodic forcing and the wavelength of the pattern of the respective system. Both sets of coupled amplitude equations are derived by a perturbative method from the Lengyel-Epstein model describing a chemical reaction showing Turing patterns, which gives us the opportunity to relate the generic response scenarios to a specific pattern forming system. The nonlinear competition between stripe patterns and distorted hexagons is explored and their range of existence, stability and coexistence is determined. Whereas without modulations hexagonal patterns are always preferred near onset of pattern formation, single mode solutions (stripes) are favored close to threshold for modulation amplitudes beyond some critical value. Hence distorted hexagons only occur in a finite range of the control parameter and their interval of existence shrinks to zero with increasing values of the modulation amplitude. Furthermore depending on the modulation amplitude the transition between stripes and distorted hexagons is either sub- or supercritical.Comment: 10 pages, 12 figures, submitted to Physical Review

Planform selection in two-layer Benard-Marangoni convection

Benard-Marangoni convection in a system of two superimposed liquids is investigated theoretically. Extending previous studies the complete hydrodynamics of both layers is treated and buoyancy is consistently taken into account. The planform selection problem between rolls, squares and hexagons is investigated by explicitly calculating the coefficients of an appropriate amplitude equation from the parameters of the fluids. The results are compared with recent experiments on two-layer systems in which squares at onset have been reported.Comment: 17 pages, 7 figures, oscillatory instability included, typos corrected, references adde

Defect Chaos of Oscillating Hexagons in Rotating Convection

Using coupled Ginzburg-Landau equations, the dynamics of hexagonal patterns with broken chiral symmetry are investigated, as they appear in rotating non-Boussinesq or surface-tension-driven convection. We find that close to the secondary Hopf bifurcation to oscillating hexagons the dynamics are well described by a single complex Ginzburg-Landau equation (CGLE) coupled to the phases of the hexagonal pattern. At the bandcenter these equations reduce to the usual CGLE and the system exhibits defect chaos. Away from the bandcenter a transition to a frozen vortex state is found.Comment: 4 pages, 6 figures. Fig. 3a with lower resolution no