Scalings and structures in turbulent Couette-Taylor flow

The scaling of velocity structure functions in Couette-Taylor flow [Lewis and Swinney, Phys. Rev. E 59, 5457 (1999)] is revisited to obtain more accurate values of the scaling exponents for the Reynolds number range investigated, 12,000 to 540,000 (Taylor Reynolds numbers, 34<R(lambda)<220). Systematic convergence of the statistics with increasing sample size is examined, and the uncertainty of the scaling exponents is assessed. At all Reynolds numbers the data support the hierarchical symmetry proposed by She and Leveque [Phys. Rev. Lett. 72, 336 (1994)]. The She-Leveque constant beta has a value of 0.83, indicating greater intermittency in Couette-Taylor turbulence than in free jets, where beta=0.87. The constant gamma, which is a measure of the degree of singularity of the most intermittent structure, decreases from 0.14 for R<10(5) to 0.10 for R>10(5); this transition corresponds to a visually observed break up of the Taylor vortex roll structure with increasing R.

Spiral patterns in oscillated granular layers

Cell-filling spiral patterns are observed in a vertically oscillated layer of granular material when the oscillation amplitude is suddenly increased from below the onset of pattern formation into the region where stripe patterns appear for quasistatic increases in amplitude. These spirals are transients and decay to stripe patterns with defects. A transient spiral defect chaos state is also observed. We describe the behavior of the spirals, and the way in which they form and decay. Our results are compared with those for similar spiral patterns in Rayleigh-Bénard convection in fluids.

Measuring nonextensitivity parameters in a turbulent Couette-Taylor flow

We investigate probability density functions of velocity differences at different distances r measured in a Couette-Taylor flow for a range of Reynolds numbers Re. There is good agreement with the predictions of a theoretical model based on nonextensive statistical mechanics (where the entropies are nonadditive for independent subsystems). We extract the scale-dependent nonextensitivity parameter q(r,Re) from the laboratory data.

Suppression of dripping from a ceiling

An isothermal layer suspended from a surface is gravitationally (Rayleigh-Taylor) unstable. We find that, when a vertical temperature difference DeltaT above a critical value (DeltaT)(c) is imposed across the liquid-gas layer system (heated from below), the restoring force provided by the temperature-dependent surface tension (thermocapillarity) can stabilize the layer. Our measurements of the most unstable wave number for DeltaT<(DeltaT)(c) agree well with our linear stability analysis. The instability occurs at long wavelengths: the most unstable wavelength at (DeltaT)(c) is infinite.

Four-phase patterns in forced oscillatory systems

We investigate pattern formation in self-oscillating systems forced by an external periodic perturbation. Experimental observations and numerical studies of reaction-diffusion systems and an analysis of an amplitude equation are presented. The oscillations in each of these systems entrain to rational multiples of the perturbation frequency for certain values of the forcing frequency and amplitude. We focus on the subharmonic resonant case where the system locks at one-fourth the driving frequency, and four-phase rotating spiral patterns are observed at low forcing amplitudes. The spiral patterns are studied using an amplitude equation for periodically forced oscillating systems. The analysis predicts a bifurcation (with increasing forcing) from rotating four-phase spirals to standing two-phase patterns. This bifurcation is also found in periodically forced reaction-diffusion equations, the FitzHugh-Nagumo and Brusselator models, even far from the onset of oscillations where the amplitude equation analysis is not strictly valid. In a Belousov-Zhabotinsky chemical system periodically forced with light we also observe four-phase rotating spiral wave patterns. However, we have not observed the transition to standing two-phase patterns, possibly because with increasing light intensity the reaction kinetics become excitable rather than oscillatory.

Resonant phase patterns in a reaction-diffusion system

Resonance regions similar to the Arnol'd tongues found in single oscillator frequency locking are observed in experiments using a spatially extended periodically forced Belousov-Zhabotinsky system. We identify six distinct 2:1 subharmonic resonant patterns and describe them in terms of the position-dependent phase and magnitude of the oscillations. Some experimentally observed features are also found in numerical studies of a forced Brusselator reaction-diffusion model.

Transition from spirals to defect-mediated turbulence driven by a doppler instability

A transition from rotating chemical spirals to turbulence is observed in experiments on the Belousov-Zhabotinsky reaction. The transition occurs when the waves near the spiral tip spontaneously break, generating defects. Measurements reveal that this defect-mediated turbulence is caused by the Doppler effect on the traveling waves. The observations are in good accord with numerical simulations and theory.

Transport coefficients for granular media from molecular dynamics simulations

Under many conditions, macroscopic grains flow like a fluid; kinetic theory predicts continuum equations of motion for this granular fluid. In order to test the theory, we perform event-driven molecular simulations of a two-dimensional gas of inelastic hard disks, driven by contact with a heat bath. Even for strong dissipation, high densities, and small numbers of particles, we find that continuum theory describes the system well. With a bath that heats the gas homogeneously, strong velocity correlations produce a slightly smaller energy loss due to inelastic collisions than that predicted by kinetic theory. With an inhomogeneous heat bath, thermal or velocity gradients are induced. Determination of the resulting fluxes allows calculation of the thermal conductivity and shear viscosity, which are compared to the predictions of granular kinetic theory, and which can be used in continuum modeling of granular flows. The shear viscosity is close to the prediction of kinetic theory, while the thermal conductivity can be overestimated by a factor of 2; in each case, transport is lowered with increasing inelasticity.

Instability of the Kolmogorov flow in a soap film

We examine the instability of a soap film flow driven by a time-independent force that is spatially periodic in the direction perpendicular to the forcing (Kolmogorov flow). Linear stability analysis of an idealized model of this flow predicts a critical Reynolds number R(c) is approximately equal to the square root of 2. In our soap film experiment, we find a critical value R(c) is approximately equal to 70. This discrepancy can be ascribed to frictional effects from viscous coupling of gas to the film, which is neglected in the idealized model. The kinematic viscosity of the surrounding gas and the thickness of gas layers on each side of the soap film are varied in the experiments to better understand these frictional effects. Our observations indicate that flow in the soap film cannot be decoupled from flow in the surrounding gas.

Velocity structure functions, scaling, and transitions in high-Reynolds-number Couette-Taylor flow

Flow between concentric cylinders with a rotating inner cylinder is studied for Reynolds numbers in the range 2x10(3)<R<10(6) (Taylor Reynolds numbers, 10 < R(lambda)< 290) for a system with radius ratio eta=0.724. Even at the highest Reynolds number studied, the energy spectra do not show power law scaling (i.e., there is no inertial range), and the dissipation length scale is surprisingly large. Nevertheless, the velocity structure functions calculated using extended self-similarity exhibit clear power-law scaling. The structure function exponents zeta(p) fit Kolmogorov's log-normal model within the experimental uncertainty, zeta(p)=(p/3) [1+(mu/6)(3-p)] (for p < or =10) with mu=0.27. These zeta(p) values are close to those found in other flows. Measurements of torque scaling are presented that are an order of magnitude more accurate than those previously reported [Lathrop et al., Phys Rev. A 46, 6390 (1992)]. Measurements of velocity in the fluid core reveal the presence of azimuthal traveling waves up to the highest Reynolds numbers examined. These waves show evidence of a transition at R(T)=1.3 x 10(4); this transition was observed previously in measurements of torque, but our wave velocity and wall shear stress measurements provide the first evidence from local quantities of the transition at R(T). Velocity measurements indicate that at R(T) there is a change in the coherent structures of the core flow; this is consistent with our analyses of the scaling of the torque. Our measurements were made at two aspect ratios, and no significant dependence on aspect ratio was observable for R > R(T).

Transitions between blocked and zonal flows in a rotating annulus with topography

The mid-latitude atmosphere is dominated by westerly, nearly zonal flow. Occasionally, this flow is deflected poleward by blocking anticyclones that persist for 10 days or longer. Experiments in a rotating annulus used radial pumping to generate a zonal jet under the action of the Coriolis force. In the presence of two symmetric ridges at the bottom of the annulus, the resulting flows were nearly zonal at high forcing or blocked at low forcing. Intermittent switching between blocked and zonal patterns occurs because of the jet's interaction with the topography. These results shed further light on previous atmospheric observations and numerical simulations.

Pattern Formation by Interacting Chemical Fronts

Experiments on a bistable chemical reaction in a continuously fed thin gel layer reveal a new type of spatiotemporal pattern, one in which fronts propagate at a constant speed until they reach a critical separation (typically 0.4 millimeter) and stop. The resulting asymptotic state is a highly irregular stationary pattern that contrasts with the regular patterns such as hexagons, squares, and stripes that have been observed in many nonequilibrium systems. The observed patterns are initiated by a finite amplitude perturbation rather than through spontaneous symmetry breaking.

Dimensions of Xf virus from its rotational and translational diffusion coefficients

Measurements on monodisperse preparations of the filamentous virus Xf give 17.3 +/- 0.6 s-1 for its rotational diffusion coefficient in 1 mM sodium phosphate, pH 7.5 at 20 degrees C and (2.53 +/- 0.06) X 10(-8) cm2 s-1 for its translational diffusion coefficient in 0.15 M NaCl and 0.015 M sodium phosphate, pH 7, at 25 degrees C. These coefficients yield a length of 980 +/- 30 nm and a diameter of 7.2 +/- 1.5 nm for the virus in solution when used to solve simultaneously the two Broersma equations for the diffusion of rigid rods.