Knots and Random Walks in Vibrated Granular Chains

We study experimentally statistical properties of the opening times of knots in vertically vibrated granular chains. Our measurements are in good qualitative and quantitative agreement with a theoretical model involving three random walks interacting via hard core exclusion in one spatial dimension. In particular, the knot survival probability follows a universal scaling function which is independent of the chain length, with a corresponding diffusive characteristic time scale. Both the large-exit-time and the small-exit-time tails of the distribution are suppressed exponentially, and the corresponding decay coefficients are in excellent agreement with the theoretical values.Comment: 4 pages, 5 figure

Hysteresis at low Reynolds number: the onset of 2D vortex shedding

Hysteresis has been observed in a study of the transition between laminar flow and vortex shedding in a quasi-two dimensional system. The system is a vertical, rapidly flowing soap film which is penetrated by a rod oriented perpendicular to the film plane. Our experiments show that the transition from laminar flow to a periodic K\'arm\'an vortex street can be hysteretic, i.e. vortices can survive at velocities lower than the velocity needed to generate them.Comment: RevTeX file 4 pages + 5 (encapsulated postscript) figures. to appear in Phys.Rev.E, Rapid Communicatio

Regular and chaotic flow patterns upon impulsive spin-up of a Rayleigh-Benard convection cell

A cylindrical, completely enclosed Rayleigh-Benard convection cell with radius-to-height ratio {Gamma}={1/2} is subjected to impulsive spin-up about its vertical axis. The authors study produces TLC (thermochromic liquid crystal) temperature measurements and PIV (particle image velocimetry) velocity reconstruction of the transient state between the two regimes of turbulent convection corresponding to the cell at rest and in steady rotation. The most persistent transient feature emerging is a sharply defined ringlike pattern characterized by a decrease in temperature and high azimuthal shear. The latter leads to formation of Kelvin-Helmholz vortices. Initially azimuthally regular, the pattern of these vortices loses its regularity and thus completes the transition to rotating convection state

Flow structure in a Rayleigh-Benard cell upon impulsive spin-up

We investigate convection in a cylindrical Rayleigh-Benard cell with radius-to-height ratio {Gamma} = {1/2}. The cell is subjected to impulsive spin-up about its vertical axis. We use TLC (thermochromic liquid crystal) for temperature field measurements and PIV (particle image velocimetry) for the velocity reconstruction of the transition in the range of Rayleigh numbers R from 5 x 10{sup 7} to 5 x 10{sup 8} and Taylor numbers Ta from 0 up to 2.4 x 10{sup 10}. The initial (at rest) and the final (in steady rotation) vection. The most persistent transient feature emerging is a sharply defined ringlike pattern or concentric patterns characterized by a decrease in temperature, axial velocity directed downward and high azimuthal shear. The latter leads to formation of an azimuthally regular structure of Kelvin-Helmholz vortices. During the next stage of the transition, the vortical structure loses azimuthal regularity and the pattern characteristic of turbulent rotating convection forms

Vortex structure in rotating Rayleigh-Benard convection

The authors investigate the flow patterns in a cylindrical rotating Rayleigh-Benard convection cell with radius-to-height ratio {Gamma} = 0.5. The Rayleigh number R is 2 x 10{sup 8}, the dimensionless rotation rate {Omega} varies from 10{sup 4} to 5 x 10{sup 4}, and the convective Rossby number Ro is between 2 and 0.4. Measurements of the velocity field in the volume adjacent to the top of the cell are acquired with a scanning particle image velocimetry (PIV) system. The authors present quantitative results for velocity and vorticity of the cyclonic and anticyclonic vortices characterizing the convection, as well as for the dependence of the vortex size on the rotation rate and variation of vorticity with depth

Growth rate and transition to turbulence of a gas curtain

The authors conduct shock-tube experiments to investigate Richtmyer-Meshkov (RM) instability of a narrow curtain of heavy gas (SF{sub 6}) embedded in lighter gas (air). Initial perturbations of the curtain can be varied, producing different flow patterns in the subsequent evolution of the curtain. Multiple-exposure video flow visualization provides images of the growth of the instability and its transition to turbulence, making it possible to extract quantitative information such as the width of the perturbed curtain. They demonstrate that the width of the curtain with initial perturbation on the downstream side is non-monotonic. As the initial perturbation undergoes phase inversion, the width of the curtain actually decreases before beginning to grow as the RM instability evolves

Mixing transition in a shocked variable-density flow

We measure two-dimensional velocity and density fluctuations in a shock-driven heavy gas curtain for three different incident Mach numbers (M = 1.21, 1.36, and 1.50) and a fixed initial perturbation. We study the time evolution of the velocity and density fields and observe two different mixing transitions in this unsteady flow. The first transition is caused by small-scale mixing in vortex cores, while the second transition is related to increased homogenization across the mixing layer and a drive towards isotropy. By measuring the anisotropy of the velocity fluctuations and the evolution of the turbulent kinetic energy, we are able to assess the anisotropy of the flow. For the first time in Richtmyer-Meshkov (RM) flows, we measure and compare turbulent length scales derived from both the density and velocity field measurements, and we find ratios of Liepmann-Taylor to inner-viscous scales (lambda(L)/lambda(nu)) that are inconsistent with those found using Reynolds number scaling based on circulation, Re-Gamma, or based on turbulent kinetic energy, Re-K. At late times, Re-K better reflects the decay of the mixing field than Reynolds numbers that are based upon mixing width or circulation. We also estimate the time evolution of dissipation and Kolmogorov scales for the first time in RM flows. When we estimate the Taylor microscale (lambda(T)) for our experiments using both density and velocity, the density microscale agrees well with the relationship lambda(T) = root 10 delta Re-1/2 where Re = Re-K and delta is the mixing layer width, but the velocity-based Taylor microscale follows a new scaling of lambda(T) = 10 delta Re-1/2. (C) 2015 AIP Publishing LLC