Transition to weak turbulence via spatiotemporal intermittency in the Taylor-Dean system

Slow diffusive structure in Nikolaevskii turbulence

Weak turbulence has been investigated in nonlinear-nonequilibrium physics to understand universal characteristics near the transition point of ordered and disordered states. Here the one-dimensional Nikolaevskii turbulence, which is a mathematical model of weak turbulence, is studied theoretically. We calculate the velocity field of the Nikolaevskii turbulence assuming a convective structure and carry out tagged-particle simulations in the flow to clarify the Nikolaevskii turbulence from the Lagrangian description. The tagged particle diffuses in the disturbed flow and the diffusion is superdiffusive in an intermediate timescale between ballistic and normal-diffusive scale. The diffusion of the slow structure is characterized by the power law for the control parameter near the transition point of the Nikolaevskii turbulence, suggesting that the diffusive characteristics of the slow structure remain scale invariant. We propose a simplified model, named two-scale Brownian motion, which reveals a hierarchy in the Nikolaevskii turbulence.

Change of criticality in a prototypical thermoacoustic system

In this paper, we report on the existence of the phenomenon of change of criticality in a horizontal Rijke tube, a prototypical thermoacoustic system. In the experiments, the phenomenon is shown to occur as the criticality of the Hopf bifurcation changes with varying air flow rates in the system. The dynamics of a nonlinear system exhibiting Hopf bifurcation can be described using a Stuart-Landau equation (SLE) in the vicinity of the bifurcation point. The criticality of Hopf bifurcations can be determined by the Landau constant of the Stuart-Landau equation, which represents the effect of nonlinearities in the system. We propose an SLE to model the bifurcations seen in the horizontal Rijke tube. We identify a rescaled version of Strouhal number as the Landau constant, which determines the criticality of the bifurcation in the present study.

Relaxation with long-period oscillation in defect turbulence of planar nematic liquid crystals

Through experiments, we studied defect turbulence, a type of spatiotemporal chaos in planar systems of nematic liquid crystals, to clarify the chaotic advection of weak turbulence. In planar systems of large aspect ratio, structural relaxation, which is characterized by the dynamic structure factor, exhibits a long-period oscillation that is described well by a combination of a simple exponential relaxation and underdamped oscillation. The simple relaxation arises as a result of the roll modulation while the damped oscillation is manifest in the repetitive gliding of defect pairs in a local area. Each relaxation is derived analytically by the projection operator method that separates turbulent transport into a macroscopic contribution and fluctuations. The analysis proposes that the two relaxations are not correlated. The nonthermal fluctuations of defect turbulence are consequently separated into two independent Markov processes. Our approach sheds light on diversity and universality from a unified viewpoint for weak turbulence.

Lagrangian chaos and particle diffusion in electroconvection of planar nematic liquid crystals

Two types of spatiotemporal chaos in the electroconvection of nematic liquid crystals, such as defect turbulence and spatiotemporal intermittency, have been statistically investigated according to the Lagrangian picture. Here fluctuations are traced using the motion of a single particle driven by chaotic convection. In the defect turbulence (fluctuating normal rolls), a particle is mainly trapped in a roll but sometimes jumps to a neighboring roll. Its activation energy is then obtained from the jumping (hopping) rate. This research clarifies that diffusion in the defect turbulence regime in electroconvection can be regarded as a kind of hopping process. The spatiotemporal intermittency appears as a coexistent state of ordered grid domains and turbulent domains. The motion of a single particle shows weak and strong diffusion, respectively, in the ordered and turbulent domains. The diffusion characteristics intermittently change from one to another with certain durations as the domains change. This research has found that the distribution function of the duration that a particle remains in an ordered area has a power-law decay for which the index is different from that obtained by the Eulerian measurement.

Nature of laminar-turbulence intermittency in shear flows

In pipe, channel, and boundary layer flows turbulence first occurs intermittently in space and time: at moderate Reynolds numbers domains of disordered turbulent motion are separated by quiescent laminar regions. Based on direct numerical simulations of pipe flow we argue here that the spatial intermittency has its origin in a nearest neighbor interaction between turbulent regions. We further show that in this regime turbulent flows are intrinsically intermittent with a well-defined equilibrium turbulent fraction but without ever assuming a steady pattern. This transition scenario is analogous to that found in simple models such as coupled map lattices. The scaling observed implies that laminar intermissions of the turbulent flow will persist to arbitrarily large Reynolds numbers.

Transition to turbulence in a flow of a shear-thinning viscoelastic solution in a Taylor-Couette cell

The transition to turbulence in a flow of semidilute shear-thinning viscoelastic solution with a moderate elasticity was investigated in the Taylor-Couette system with a fixed outer cylinder. As the cylinder rotation frequency increases, the base flow bifurcates to a pattern of ribbons and then to disordered oscillations (DOs). Within these DOs, we have identified two particular regimes of turbulence: spatiotemporal intermittency (STI) followed by inertioelastic turbulence (IET) with a net transition between them. This transition is evidenced by a sharp peak of a diffusion velocity and a Weissenberg number.

Experimental realization of directed percolation criticality in turbulent liquid crystals

This is a comprehensive report on the phase transition between two turbulent states of electroconvection in nematic liquid crystals, which was recently found by the authors to be in the directed percolation (DP) universality class [K. A. Takeuchi, Phys. Rev. Lett. 99, 234503 (2007)]. We further investigate both static and dynamic critical behaviors of this phase transition, measuring a total of 12 critical exponents, 5 scaling functions, and 8 scaling relations, all in full agreement with those characterizing the DP class in 2+1 dimensions. Developing an experimental technique to create a seed of topological-defect turbulence by pulse laser, we confirm in particular the rapidity symmetry, which is a basic but nontrivial consequence of the field-theoretic approach to DP. This provides a clear experimental realization of this outstanding truly out-of-equilibrium universality class, dominating most phase transitions into an absorbing state.

Directed percolation criticality in turbulent liquid crystals

We experimentally investigate the critical behavior of a phase transition between two topologically different turbulent states of electrohydrodynamic convection in nematic liquid crystals. The statistical properties of the observed spatiotemporal intermittency regimes are carefully determined, yielding a complete set of static critical exponents in full agreement with those defining the directed percolation class in 2+1 dimensions. This constitutes the first clear and comprehensive experimental evidence of an absorbing phase transition in this prominent nonequilibrium universality class.

Chaotic saddles at the onset of intermittent spatiotemporal chaos

In a recent study [Rempel and Chian, Phys. Rev. Lett. 98, 014101 (2007)], it has been shown that nonattracting chaotic sets (chaotic saddles) are responsible for intermittency in the regularized long-wave equation that undergoes a transition to spatiotemporal chaos (STC) via quasiperiodicity and temporal chaos. In the present paper, it is demonstrated that a similar mechanism is present in the damped Kuramoto-Sivashinsky equation. Prior to the onset of STC, a spatiotemporally chaotic saddle coexists with a spatially regular attractor. After the transition to STC, the chaotic saddle merges with the attractor, generating intermittent bursts of STC that dominate the post-transition dynamics.

Localized intermittent short-wavelength bursts in the high-radius ratio limit of the Taylor-Couette system

We have explored flow states of the Taylor-Couette system in the high radius ratio limit (0.99) with only the inner cylinder rotating. The usual Taylor vortices and wavy vortices were found, but the transition to higher states is interrupted by the emergence of intermittent short-wavelength bursts. This flow state is distinct from previously observed bursting phenomena found at lower radius ratios, while it is similar in appearance to states found in inclined layer convection.

Synchronized chaotic intermittent and spiking behavior in coupled map chains

We study phase synchronization effects in a chain of nonidentical chaotic oscillators with a type-I intermittent behavior. Two types of parameter distribution, linear and random, are considered. The typical phenomena are the onset and existence of global (all-to-all) and cluster (partial) synchronization with increase of coupling. Increase of coupling strength can also lead to desynchronization phenomena, i.e., global or cluster synchronization is changed into a regime where synchronization is intermittent with incoherent states. Then a regime of a fully incoherent nonsynchronous state (spatiotemporal intermittency) appears. Synchronization-desynchronization transitions with increase of coupling are also demonstrated for a system resembling an intermittent one: a chain of coupled maps replicating the spiking behavior of neurobiological networks.

Defects and spatiotemporal disorder in a pattern of falling liquid columns

Disordered regimes of a one-dimensional pattern of liquid columns hanging below an overflowing circular dish are investigated experimentally. The interaction of two basic dynamical modes (oscillations and drift) combined with the occurrence of defects (birth of new columns, disappearances by coalescences of two columns) leads to spatiotemporal chaos. When the flow rate is progressively increased, a continuous transition between transient and permanent chaos is pointed into evidence. We introduce the rate of defects as the sole relevant quantity to quantify this "turbulence" without ambiguity. Statistics on both transient and endlessly chaotic regimes enable to define a critical flow rate around which exponents are extracted. Comparisons are drawn with other interfacial pattern-forming systems, where transition towards chaos follows similar steps. Qualitatively, careful examinations of the global dynamics show that the contamination processes are nonlocal and involve the propagation of blocks of elementary laminar states (such as propagative domains or local oscillations), emitted near the defects, which turn out to be essential ingredients of this self-sustained disorder.

Critical exponents of directed percolation measured in spatiotemporal intermittency

An experimental system showing a transition to spatiotemporal intermittency is presented. It consists of a ring of hundred oscillating ferrofluidic spikes. Four of five of the measured critical exponents of the system agree with those obtained from a theoretical model of directed percolation.

Spatiotemporal intermittency and scaling laws in inhomogeneous coupled map lattices

We study the phenomenon of intermittency in an inhomogeneous lattice of coupled maps where the inhomogeneity appears in the form of different values of the map parameter at adjacent sites. This system exhibits spatiotemporal intermittency as well as purely spatial intermittency accompanied by temporal periodicity in different regions of the parameter space. Both types of intermittency appear as a result of bifurcations of codimension two in such systems. We identify the types of bifurcations that are seen. The intermittency near the bifurcation points and lines is associated with power-law distributions for the laminar lengths. The scaling laws for the laminar length distributions are obtained. Two distinct types of scaling behavior characterized by power laws with exponents that fall in two distinct ranges can be seen in the neighborhood of codimension-two bifurcation points. Additionally we find two crossover exponents.