Turbulence characteristics of the B\"{o}dewadt layer in a large enclosed rotor-stator system

A three-dimensional (3D) direct numerical simulation is combined with a laboratory study to describe the turbulent flow in an enclosed annular rotor-stator cavity characterized by a large aspect ratio G=(b-a)/h=18.32 and a small radius ratio a/b=0.152, where a and b are the inner and outer radii of the rotating disk and h is the interdisk spacing. The rotation rate Omega under consideration is equivalent to the rotational Reynolds number Re=Omegab2/nu=9.5 x 104, where nu is the kinematic viscosity of the fluid. This corresponds to a value at which an experiment carried out at the laboratory has shown that the stator boundary layer is turbulent, whereas the rotor boundary layer is still laminar. Comparisons of the 3D computed solution with velocity measurements have given good agreement for the mean and turbulent fields. The results enhance evidence of weak turbulence at this Reynolds number, by comparing the turbulence properties with available data in the literature. An approximately self-similar boundary layer behavior is observed along the stator side. The reduction of the structural parameter a1 under the typical value 0.15 and the variation in the wall-normal direction of the different characteristic angles show that this boundary layer is three-dimensional. A quadrant analysis of conditionally averaged velocities is performed to identify the contributions of different events (ejections and sweeps) on the Reynolds shear stress producing vortical structures. The asymmetries observed in the conditionally averaged quadrant analysis are dominated by Reynolds stress-producing events in this B\"{o}dewadt layer. Moreover, case 1 vortices (with a positive wall induced velocity) are found to be the major source of generation of special strong events, in agreement with the conclusions of Lygren and Andersson.Comment: 16 page

Green's function probe of a static granular piling

We present an experiment which aim is to investigate the mechanical properties of a static granular assembly. The piling is an horizontal 3D granular layer confined in a box, we apply a localized extra force at the surface and the spatial distribution of stresses at the bottom is obtained (the mechanical Green's function). For different types of granular media, we observe a linear pressure response which profile shows one peak centered at the vertical of the point of application. The peak's width increases linearly when increasing the depth. This green function seems to be in -at least- qualitative agreement with predictions of elastic theory.Comment: 9 pages, 3 .eps figures, submitted to PR

Stresses in silos: Comparison between theoretical models and new experiments

We present precise and reproducible mean pressure measurements at the bottom of a cylindrical granular column. If a constant overload is added, the pressure is linear in overload and nonmonotonic in the column height. The results are {\em quantitatively} consistent with a local, linear relation between stress components, as was recently proposed by some of us. They contradict the simplest classical (Janssen) approximation, and may pose a rather severe test of competing models.Comment: 4 pages, 2 figures, final version to appear in Phys. Rev. Let

Imprinting the memory into paste and its visualization as crack patterns in drying process

In the drying process of paste, we can imprint into the paste the order how it should be broken in the future. That is, if we vibrate the paste before it is dried, it remembers the direction of the initial external vibration, and the morphology of resultant crack patterns is determined solely by the memory of the direction. The morphological phase diagram of crack patterns and the rheological measurement of the paste show that this memory effect is induced by the plasticity of paste.Comment: 4 pages, 3 figures, submitted to JPS

Stress Transmission through Three-Dimensional Ordered Granular Arrays

We measure the local contact forces at both the top and bottom boundaries of three-dimensional face-centered-cubic and hexagonal-close-packed granular crystals in response to an external force applied to a small area at the top surface. Depending on the crystal structure, we find markedly different results which can be understood in terms of force balance considerations in the specific geometry of the crystal. Small amounts of disorder are found to create additional structure at both the top and bottom surfaces.Comment: 9 pages including 9 figures (many in color) submitted to PR

Fluctuation of the Top Location and Avalanches in the Formation Process of a Sandpile

We investigate the formation processes of a sandpile using numerical simulation. We find a new relation between the fluctuation of the motion of the top and the surface state of a sandpile. The top moves frequently as particles are fed one by one every time interval T. The time series of the top location has the power spectrum which obeys a power law, S(f)~f^{\alpha}, and its exponent \alpha depends on T and the system size w. The surface state is characterized by two time scales; the lifetime of an avalanche, T_{a}, and the time required to cause an avalanche, T_{s}. The surface state is fluid-like when T_{a}~T_{s}, and it is solid-like when T_{a}<<T_{s}. Our numerical results show that \alpha is a function of T_{s}/T_{a}.Comment: 15 pages, 13 figure

Footprints in Sand: The Response of a Granular Material to Local Perturbations

We experimentally determine ensemble-averaged responses of granular packings to point forces, and we compare these results to recent models for force propagation in a granular material. We used 2D granular arrays consisting of photoelastic particles: either disks or pentagons, thus spanning the range from ordered to disordered packings. A key finding is that spatial ordering of the particles is a key factor in the force response. Ordered packings have a propagative component that does not occur in disordered packings.Comment: 5 pages, 4 eps figures, Phys. Rev. Lett. 87, 035506 (2001

Morphology of two dimensional fracture surface

We consider the morphology of two dimensional cracks observed in experimental results obtained from paper samples and compare these results with the numerical simulations of the random fuse model (RFM). We demonstrate that the data obey multiscaling at small scales but cross over to self-affine scaling at larger scales. Next, we show that the roughness exponent of the random fuse model is recovered by a simpler model that produces a connected crack, while a directed crack yields a different result, close to a random walk. We discuss the multiscaling behavior of all these models.Comment: slightly revise

Jamming and Fluctuations in Granular Drag

We investigate the dynamic evolution of jamming in granular media through fluctuations in the granular drag force. The successive collapse and formation of jammed states give a stick-slip nature to the fluctuations which is independent of the contact surface between the grains and the dragged object -- thus implying that the stress-induced collapse is nucleated in the bulk of the granular sample. We also find that while the fluctuations are periodic at small depths, they become "stepped" at large depths, a transition which we interpret as a consequence of the long-range nature of the force chains.Comment: 7 pages, 4 figures, RevTe

Response of a Hexagonal Granular Packing under a Localized External Force: Exact Results

We study the response of a two-dimensional hexagonal packing of massless, rigid, frictionless spherical grains due to a vertically downward point force on a single grain at the top layer. We use a statistical approach, where each mechanically stable configuration of contact forces is equally likely. We show that this problem is equivalent to a correlated $q$-model. We find that the response is double-peaked, where the two peaks, sharp and single-grain diameter wide, lie on the two downward lattice directions emanating from the point of the application of the external force. For systems of finite size, the magnitude of these peaks decreases towards the bottom of the packing, while progressively a broader, central maximum appears between the peaks. The response behaviour displays a remarkable scaling behaviour with system size $N$: while the response in the bulk of the packing scales as $\frac{1}{N}$, on the boundary it is independent of $N$, so that in the thermodynamic limit only the peaks on the lattice directions persist. This qualitative behaviour is extremely robust, as demonstrated by our simulation results with different boundary conditions. We have obtained expressions of the response and higher correlations for any system size in terms of integers corresponding to an underlying discrete structure.Comment: Accepted for publication in JStat; 33 pages, 10 figures; Section 2.2 reorganized and rewritten; Details about the simulation procedure added in Sec.3.1. ; A new section, summarizing the final results and the calculation procedure adde