Passive tracer dynamics in 4 point-vortex flow

The advection of passive tracers in a system of 4 identical point vortices is studied when the motion of the vortices is chaotic. The phenomenon of vortex-pairing has been observed and statistics of the pairing time is computed. The distribution exhibits a power-law tail with exponent ∼ 3.6 implying finite average pairing time. This exponents is in agreement with its computed analytical estimate of 3.5. Tracer motion is studied for a chosen initial condition of the vortex system. Accessible phase space is investigated. The size of the cores around the vortices is well approximated by the minimum inter-vortex distance and stickiness to these cores is observed. We investigate the origin of stickiness which we link to the phenomenon of vortex pairing and jumps of tracers between cores. Motion within the core is considered and fluctuations are shown to scale with tracer-vortex distance r as r ⁶. No outward or inward diffusion of tracers are observed. This investigation allows the separation of the accessible phase space in four distinct regions, each with its own specific properties: the region within the cores, the reunion of the periphery of all cores, the region where vortex motion is restricted and finally the far-field region. We speculate that the stickiness to the cores induced by vortex-pairings influences the long-time behavior of tracers and their anomalous diffusion. Received 28 September 2000 and Received in final form 9 February 2001     

Lagrangian dispersion and heat transport in convective turbulence

Lagrangian studies of the local temperature mixing and heat transport in turbulent Rayleigh-Bénard convection are presented, based on three-dimensional direct numerical simulations. Contrary to vertical pair distances, the temporal growth of lateral pair distances agrees with the Richardson law, but yields a smaller Richardson constant due to correlated pair motion in plumes. Our results thus imply that Richardson dispersion is also found in anisotropic turbulence. We find that extremely large vertical accelerations appear less frequently than lateral ones and are not connected with rising or falling thermal plumes. The height-dependent joint Lagrangian statistics of vertical acceleration and local heat transfer allow us to identify a zone which is dominated by thermal plume mixing.     

Pair dispersion in turbulence: the subdominant role of scaling

The mixing properties of turbulent flows are, at first order, related to the dynamics of separation of particle pairs. Scaling laws for the evolution in time of the mean distance between particle pairs (t) have been proposed since the pioneering work of Richardson. We analyze a model which shares some features with 3D experimental and numerical turbulence, and suggest that pure scaling laws are only subdominant. The dynamics is dominated by a very wide distribution of "delay times" t(d), the duration for which particle pairs remain together before their separation increases significantly. The delay time distribution is exponential for small separations and evolves towards a flat distribution at large separations. The observed (t) behavior is best understood as an average over separations that individually follow the Richardson-Obukhov scaling, r(2) ∝ t(3), but each only after a fluctuating time delay t(d), where t(d) is distributed uniformly.     

Evolution of the Probability Measure for the Majda Model: New Invariant Measures and Breathing PDFs

In 1993, Majda proposed a simple, random shear model from which scalar intermittency was rigorously predicted for the invariant probability measure of passive tracers. In this work, we present an integral formulation for the tracer measure, which leads to a new, comprehensive study on its temporal evolution based on Monte Carlo simulation and direct numerical integration. An interesting, non-monotonic “breathing” phenomenon is discovered from these results and carefully defined, with a solid example for special initial data to predict such phenomenon. The signature of this phenomenon may persist at long time, characterized by the approach of the PDF core to its infinite time, invariant value. We find that this approach may be strongly dependent on the non-dimensional Péclet number, of which the invariant measure itself is independent. Further, the “breathing” PDF is recovered as a new invariant measure in a distinguished time scale in the diffusionless limit. Rigorous asymptotic analysis is also performed to identify the Gaussian core of the invariant measures, and the critical rate at which the heavy, stretched exponential regime propagates towards the tail as a function of time is calculated.     

On-Off Intermittency in Continuous Systems

On-off intermittency is investigated for the model χ= (a + Г(t))χ-χ³ with Г(t) being a stochastic force. The laminar phase distribution ω(T) is studied in the parameter space of bifurcation parameter a, noise intensity D and noise correlation time τ. It is found that increasing D may stabilize the fixed point χ= 0 and reduce the exponential tail in ω(T) for a>0. An analytical solution of the laminar phase distributions is obtained for white noise and colored noise cases, respectively, which agrees with numerical simulations well.     

Intermittency route to rheochaos in wormlike micelles with flow-concentration coupling

We show experimentally that the route to chaos is via intermittency in a shear-thinning wormlike micellar system of cetyltrimethylammonium tosylate, where the strength of flow-concentration coupling is tuned by the addition of salt sodium chloride. A Poincaré first return map of the time series and the probability distribution of laminar lengths between burst events shows that our data is consistent with type-II intermittency. The coupling of flow to concentration fluctuations is evidenced by the "butterfly" intensity pattern in small angle light scattering (SALS) measurements performed simultaneously with the rheological measurements. The scattered depolarized intensity in SALS, sensitive to orientational order fluctuations, shows the same time dependence (like intermittency) as that of shear stress.     

平均探测时间:研究单个量子点荧光现象的另一种思路

Due to photoluminescence intermittency of single colloidal quantum dots (QDs), the traditional exponential fluorescence lifetime analysis is not perfect to characterize QDs'' fluorescent emission behavior. In this work we used the time-tagged time-resolved (TTTR) mode to record the fluorescent photons from single QDs. We showed that this method is compatible with the traditional lifetime analysis. In addition, by constructing the trajectory over time and the distribution of average arrival time (AAT) of the fluorescent photons, more details about the emission behavior of QDs were revealed.     

Dispersion and mixing in quasigeostrophic turbulence

The dynamics of passive Lagrangian tracers in three-dimensional quasigeostrophic turbulence is studied numerically and compared with the behavior of two-dimensional barotropic turbulence. Despite the different Eulerian properties of the two flows, the Lagrangian dynamics of passively advected tracers in three-dimensional quasigeostrophic turbulence is very similar to that of barotropic turbulence. In both systems, coherent vortices play a major role in determining the mixing and dispersion properties. This work indicates that recent results on particle dynamics in barotropic, two-dimensional turbulence carry over to more realistic baroclinic flows, such as those encountered in the large-scale dynamics of the atmosphere and ocean.     

Band-gap fluctuations in amorphous semiconductors

The exponential absorption tails of amorphous semiconductors are described by integrating the band-to-band absorption over an exponential distribution of band-gap. This requires that the tail states are derived from the band states, and are therefore not highly localised. We show that the fluctuations required by the absorption predict the principal features of the intrinsic 1.4eV luminescence of a-Si:H. The origin of the fluctuations is attributed to ‘frozen’ phonons which constitute the amorphous short-range disorder.     

Extreme Lagrangian acceleration in confined turbulent flow

A Lagrangian study of two-dimensional turbulence for two different geometries, a periodic and a confined circular geometry, is presented to investigate the influence of solid boundaries on the Lagrangian dynamics. It is found that the Lagrangian acceleration is even more intermittent in the confined domain than in the periodic domain. The flatness of the Lagrangian acceleration as a function of the radius shows that the influence of the wall on the Lagrangian dynamics becomes negligible in the center of the domain, and it also reveals that the wall is responsible for the increased intermittency. The transition in the Lagrangian statistics between this region, not directly influenced by the walls, and a critical radius which defines a Lagrangian boundary layer is shown to be very sharp with a sudden increase of the acceleration flatness from about 5 to about 20.     

Diffusion dynamics and first passage time in a two-coupled pendulum system

We present the numerical investigation of diffusion process and features of first passage time (FPT) and mean FPT (MFPT) in a two-coupled damped and periodically driven pendulum system. The effect of amplitude of the external periodic force and phase of the force on diffusion constant, distribution of FPT, P(tFPT), and MFPT is analyzed. Normal diffusion is found. Diffusion constant is found to show power-law variation near intermittency and sudden widening crises while linear variation is observed in the quasiperiodic region. In the intermittency crisis the divergence of diffusion constant is similar to the divergence of mean bursting length. P(tFPT) of critical distances of state variable exhibit periodic multiple peaks with decaying amplitude. MFPT of critical distances also follows power-law variation. Diffusion constant and MFPT are sensitive to the phase factor of the periodic force.     

Small scale intermittency and bursting in a turbulent channel flow

The statistical properties of the streamwise velocity fluctuations in a fully developed turbulent channel flow are studied experimentally by means of single hot wire measurements. The intermittency features, studied through the scaling of the moments of the velocity structure function computed using the extended self- similarity and through the probability density function of the wavelet coefficients, are found to be dependent on the distance from the wall. The maximum intermittency effects are observed in the region between the buffer layer and the inner part of the logarithmic region where it is known that the bursting phenomenon, related to coherent structures such as low speed streaks and streamwise vortices, is the dominant dynamical feature. An eduction technique based on wavelet transform for identification of organized motion is developed and used to analyze the turbulent signals. Streamwise velocity conditional averages computed on events educed with the proposed method are reported. Events responsible for intermittency are found to consist of regions of high velocity gradients and are directly correlated with the observed increase of intermittency close to the wall.     

Turbulent transport of material particles: an experimental study of finite size effects

We present experimental Lagrangian statistics of finite sized, neutrally bouyant, particles transported in an isotropic turbulent flow. The particle's diameter is varied over turbulent inertial scales. Finite size effects are shown not to be trivially related to velocity intermittency. The global shape of the particle's acceleration probability density functions is not found to depend significantly on its size while the particle's acceleration variance decreases as it becomes larger in quantitative agreement with the classical k(-7/3) scaling for the spectrum of Eulerian pressure fluctuations in the carrier flow.     

Some features of one-soliton solutions of the Korteweg - de Vries equation

Using the method of inverse scattering problem [1, 2], we study solutions of the Korteweg - de Vries equation under initial conditions in the form of two nonsoliton pulses with not very large amplitudes. It is shown that if the distance between these pulses is not large, then they evolve to one soliton and an oscillating nonlinear tail for t → ∞. As the distance between the pulses or the pulse amplitudes increase, two solitons and an oscillating nonlinear tail are formed. Similar behavior is observed for solutions of the nonlinear Schrödinger equation. The only difference is that three, but not two, solitons are formed if the distance between two initial inphase pulses increases. The results of analytical consideration are illustrated by the numerical solution of the Korteweg - de Vries equation.     

Sound-wave coherence in atmospheric turbulence with intrinsic and global intermittency

The coherence function of sound waves propagating through an intermittently turbulent atmosphere is calculated theoretically. Intermittency mechanisms due to both the turbulent energy cascade (intrinsic intermittency) and spatially uneven production (global intermittency) are modeled using ensembles of quasiwavelets (QWs), which are analogous to turbulent eddies. The intrinsic intermittency is associated with decreasing spatial density (packing fraction) of the QWs with decreasing size. Global intermittency is introduced by allowing the local strength of the turbulence, as manifested by the amplitudes of the QWs, to vary in space according to superimposed Markov processes. The resulting turbulence spectrum is then used to evaluate the coherence function of a plane sound wave undergoing line-of-sight propagation. Predictions are made by a general simulation method and by an analytical derivation valid in the limit of Gaussian fluctuations in signal phase. It is shown that the average coherence function increases as a result of both intrinsic and global intermittency. When global intermittency is very strong, signal phase fluctuations become highly non-Gaussian and the average coherence is dominated by episodes with weak turbulence.     

Single-molecule measurements of gold-quenched quantum dots

We report the study of the quenching of quantum dots (CdSe) by gold nanoparticles at the single-molecule level. Double-stranded DNA is used as a rigid spacer to tune the distance between the two nanoparticles. The width of the fluorescent intensity distribution, monitored at different interparticle distances, reflects both the nanoparticle heterogeneity and the fluorescence intermittency of the quantum dot. The fluorescence distribution emitted by single CdSe nanocrystals can easily be distinguished from the fluorescence of partially quenched CdSe. Our results show that the distance-dependence quenching is compatible with a F?rster-type process.     

Tail resonances of Fermi-Pasta-Ulam q-breathers and their impact on the pathway to equipartition

Upon initial excitation of a few normal modes the energy distribution among all modes of a nonlinear atomic chain (the Fermi-Pasta-Ulam model) exhibits exponential localization on large time scales. At the same time, resonant anomalies (peaks) are observed in its weakly excited tail for long times preceding equipartition. We observe a similar resonant tail structure also for exact time-periodic Lyapunov orbits, coined q-breathers due to their exponential localization in modal space. We give a simple explanation for this structure in terms of superharmonic resonances. The resonance analysis agrees very well with numerical results and has predictive power. We extend a previously developed perturbation method, based essentially on a Poincare-Lindstedt scheme, in order to account for these resonances, and in order to treat more general model cases, including truncated Toda potentials. Our results give a qualitative and semiquantitative account for the superharmonic resonances of q-breathers and natural packets.     

Nonlinear instability of elementary stratified flows at large Richardson number

Elementary stably stratified flows with linear instability at all large Richardson numbers have been introduced recently by the authors [J. Fluid Mech. 376, 319-350 (1998)]. These elementary stratified flows have spatially constant but time varying gradients for velocity and density. Here the nonlinear stability of such flows in two space dimensions is studied through a combination of numerical simulations and theory. The elementary flows that are linearly unstable at large Richardson numbers are purely vortical flows; here it is established that from random initial data, linearized instability spontaneously generates local shears on buoyancy time scales near a specific angle of inclination that nonlinearly saturates into localized regions of strong mixing with density overturning resembling Kelvin-Helmholtz instability. It is also established here that the phase of these unstable waves does not satisfy the dispersion relation of linear gravity waves. The vortical flows are one family of stably stratified flows with uniform shear layers at the other extreme and elementary stably stratified flows with a mixture of vorticity and strain exhibiting behavior between these two extremes. The concept of effective shear is introduced for these general elementary flows; for each large Richardson number there is a critical effective shear with strong nonlinear instability, density overturning, and mixing for elementary flows with effective shear below this critical value. The analysis is facilitated by rewriting the equations for nonlinear perturbations in vorticity-stream form in a mean Lagrangian reference frame. (c) 2000 American Institute of Physics.