CiteULike: weeks Swinney

Experimental and numerical studies of an eastward jet over topography

Yudong Tian — 2008-06-18T01:27:04-00:00

Journal of Fluid Mechanics, Vol. 438, No. -1. (2001), pp. 129-157.

Motivated by the phenomena of blocked and zonal flows in Earth's atmosphere, we conducted laboratory experiments and numerical simulations to study the dynamics of an eastward jet flowing over wavenumber-two topography. The laboratory experiments studied the dynamical behaviour of the flow in a barotropic rotating annulus as a function of the experimental Rossby and Ekman numbers. Two distinct flow patterns, resembling blocked and zonal flows in the atmosphere, were observed to persist for long time intervals. Earlier model studies had suggested that the atmosphere's normally upstream- propagating Rossby waves can resonantly lock to the underlying topography, and that this topographic resonance separates zonal from blocked flows. In the annulus, the zonal flows did indeed have super-resonant mean zonal velocities, while the blocked flows appear subresonant. Low-frequency variability, periodic or irregular, was present in the measured time series of azimuthal velocity in the blocked regime, with dominant periodicities in the range of 6–25 annulus rotations. Oscillations have also been detected in zonal states, with smaller amplitude and similar frequency. In addition, over a large region of parameter space the two flow states exhibited spontaneous, intermittent transitions from the one to the other. We numerically simulated the laboratory flow geometry in a quasi-geostrophic barotropic model over a similar range of parameters. Both flow regimes, blocked and zonal, were reproduced in the simulations, with similar spatial and temporal characteristics, including the low-frequency oscillations associated with the blocked flow. The blocked and zonal flow patterns are present over wide ranges of forcing, topographic height, and bottom friction. For a significant portion of parameter space, both model flows are stable. Depending on the initial state, either the blocked or the zonal flow is obtained and persists indefinitely, showing the existence of multiple equilibria.

Anomalous diffusion resulting from strongly asymmetric random walks

Eric Weeks — 2008-06-15T22:33:09-00:00

Physical Review E, Vol. 57, No. 5. (1 May 1998), 4915.

We present a model of one-dimensional asymmetric random walks. Random walkers alternate between flights (steps of constant velocity) and sticking (pauses). The sticking time probability distribution function (PDF) decays as P(t)∼t-ν. Previous work considered the case of a flight PDF decaying as P(t)∼t-μ [Weeks et al., Physica D 97, 291 (1996)]; leftward and rightward flights occurred with differing probabilities and velocities. In addition to these asymmetries, the present strongly asymmetric model uses distinct flight PDFs for leftward and rightward flights: PL(t)∼t-μ and PR(t)∼t-η, with μ≠η. We calculate the dependence of the variance exponent γ (σ2∼tγ) on the PDF exponents ν, μ, and η. We find that γ is determined by the two smaller of the three PDF exponents, and in some cases by only the smallest. A PDF with decay exponent less than 3 has a divergent second moment, and thus is a Lévy distribution. When the smallest decay exponent is between 3/2 and 3, the motion is superdiffusive (1<γ<2). When the smallest exponent is between 1 and 3/2, the motion can be subdiffusive (γ<1); this is in contrast with the case with μ=η.

Transitions Between Blocked and Zonal Flows in a Rotating Annulus with Topography

Eric Weeks — 2008-06-15T22:28:54-00:00

Science, Vol. 278, No. 5343. (28 November 1997), pp. 1598-1601.

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.

Anomalous diffusion in asymmetric random walks with a quasi-geostrophic flow example

Eric Weeks — 2008-06-14T20:27:43-00:00

Physica D: Nonlinear Phenomena, Vol. 97, No. 1-3. (1 October 1996), pp. 291-310.

We present a model of one-dimensional symmetric and asymmetric random walks. The model is applied to an experiment studying fluid transport in a rapidly rotating annulus. In the model, random walkers alternate between flights (steps of constant velocity) and sticking (pauses between flights). Flight time and sticking time probability distribution functions (PDFs) have power law decays: P(t) ~ t-[mu] and t-[nu] for flights and sticking, respectively. We calculate the dependence of the variance exponent [gamma] ([sigma]2 ~ t[gamma]) on the PDF exponents [mu] and [nu]. For a broad distribution of flight times ([mu] < 3), the motion is superdiffusive (1 < [gamma] < 2), and the PDF has a divergent second moment, i.e., it is a Lévy distribution. For a broad distribution of sticking times ([nu] < 3), either superdiffusion or subdiffusion ([gamma] < 1) can occur, with qualitative differences between symmetric and asymmetric walks. For narrow PDFs ([mu] > 3, [nu] > 3), normal diffusion ([gamma] = 1) is recovered. Predictions of the model are related to experimental observations of transport in a rotating annulus. The Eulerian velocity field is chaotic, yet it is still possible to distinguish between well-defined sticking events (particles trapped in vortices) and flights (particles making long excursions in a jet). The distribution of flight lengths is well described by a power law with a divergent second moment (Lévy distribution). The observed transport is strongly asymmetric and is well described by the proposed model.

Chaotic advection in a two-dimensional flow: Lévy flights and anomalous diffusion

TH Solomon — 2008-06-14T20:25:52-00:00

Physica D: Nonlinear Phenomena, Vol. 76, No. 1-3. (1 September 1994), pp. 70-84.

Long-term particle tracking is used to study chaotic transport experimentally in laminar, chaotic, and turbulent flows in an annular tank that rotates sufficiently rapidly to insure two-dimensionality of the flow. For the laminar and chaotic velocity fields, the flow consists of v flow regimes, tracer particles stick for long times to remnants of invariant surfaces around the vortices, then make long excursions ("flights") in the jet regions. The probability distributions for the flight time durations exhibit power-law rather than exponential decays, indicating that the parrticle trajectories are described mathematically as Lévy flights (i.e. the trajectories have infinite mean square displacement per flight). Sticking time probability distributions are also characterized by power laws, as found in previous numerical studies. The mixing of an ensemble of tracer particles is superdiffusive: the variance of the displacement grows with time as t[lambda] with 1<[lambda]<2. The dependence of the diffusion exponent [lambda] and the scaling of the probability distributions are investigated for periodic and chaotic flow regimes, and the results are found to be consistent with theoretical predictions relating Lévy flights and anomalous diffusion. For a turbulent flow, the Lévy flight description no longer applies, and mixing no longer appears superdiffusive.

Phase transition in a static granular system

Matthias Schröter — 2008-04-21T22:31:55-00:00

EPL (Europhysics Letters), Vol. 78, No. 4. (2007), 44004.

We find that a column of glass beads exhibits a well-defined transition between two phases that differ in their resistance to shear. Pulses of fluidization are used to prepare static sedimented states with well-defined particle volume fractions ph in the range 0.57-0.63. The resistance to shear is determined by slowly inserting a rod into the column of beads. Force measurements and bed height measurements both indicate that the transition occurs at ph = 0.60 for a range of speeds of the rod.

Signatures of Glass Formation in a Fluidized Bed of Hard Spheres

Daniel Goldman — 2008-01-23T18:42:00-00:00

Physical Review Letters, Vol. 96, No. 14. (2006), pp. 145702-145702.

We demonstrate that a fluidized bed of hard spheres during defluidization displays properties associated with formation of a glass. The final state is rate dependent, and as this state is approached, the bed exhibits heterogeneity with increasing time and length scales. The formation of a glass results in the arrest of macroscopic particle motion and thus the loss of fluidization. Microscopic motion persists in this state, but the bed can be jammed by application of a small increase in flow rate. Thus a fluidized bed can serve as a test system for studies of glass formation and jamming.

Shocks in Supersonic Sand

Erin Rericha — 2007-09-22T19:07:02-00:00

Physical Review Letters, Vol. 88, No. 1. (17 December 2001), 014302.

We measure time-averaged velocity; density; and temperature fields for steady granular flow past a wedge. We find the flow to be supersonic with a speed of granular pressure disturbances (sound speed) equal to about 10% of the flow speed; and we observe shocks nearly identical to those in a supersonic gas. Molecular dynamics simulations of Newton’s laws yield fields in quantitative agreement with experiment. A numerical solution of Navier-Stokes–like equations agrees with a molecular dynamics simulation for experimental conditions excluding wall friction.

Observation of anomalous diffusion and Lévy flights in a two-dimensional rotating flow

TH Solomon — 2007-09-19T16:39:29-00:00

Physical Review Letters, Vol. 71, No. 24. (13 December 1993), 3975.

Chaotic transport in a laminar fluid flow in a rotating annulus is studied experimentally by tracking large numbers of tracer particles for long times. Sticking and unsticking of particles to remnants of invariant surfaces (Cantori) around vortices results in superdiffusion: The variance of the displacement grows with time as t δ with γ=1.65±0.15. Sticking and flight time probability distribution functions exhibit power-law decays with exponents 1.6±0.3 and 2.3±0.2; respectively. The exponents are consistent with theoretical predictions relating Lévy flights and anomalous diffusion.