Bloch-front turbulence: theory and experiments (original) (raw)

Bloch-Front Turbulence in a Periodically Forced Belousov-Zhabotinsky Reaction

Physical Review Letters, 2004

Experiments on a periodically forced Belousov-Zhabotinsky chemical reaction show front breakup into a state of spatiotemporal disorder involving continual events of spiral-vortex nucleation and destruction. Using the amplitude equation for forced oscillatory systems and the normal form equations for a curved front line, we identify the mechanism of front breakup and explain the experimental observations.

From labyrinthine patterns to spiral turbulence

Physical Review Letters, 1994

A new mechanism for spiral vortex nucleation in nongradient reaction di usion systems is proposed. It involves two key ingredients: An Ising-Bloch type front bifurcation and an instability of a planar front to transverse perturbations. Vortex nucleation by this mechanism plays an important role in inducing a transition from labyrinthine patterns to spiral turbulence. 05.45.+b, 82.20.Mj

Breakup of Spiral Waves into Chemical Turbulence

Physical Review Letters, 1998

Recent experiments on spiral waves in the Belousov-Zhabotinsky reaction indicate that the waves may break up sufficiently far from the core into chemical turbulence. Simulations of target patterns in the FitzHugh-Nagumo and Ginzburg-Landau models indicate that such transitions occur when the wave frequency pushes the selected wave vector into the regime of absolute Eckhaus instability. This frequency in turn depends on the control parameter and boundary conditions through the solution of a nonlinear eigenvalue problem. [S0031-9007(98)06192-4]

Complex patterns in reaction-diffusion systems: A tale of two front instabilities

Chaos: An Interdisciplinary Journal of Nonlinear Science, 1994

Two front instabilities in a reaction-di usion system are shown to lead to the formation of complex patterns. The rst is an instability to transverse modulations that drives the formation of labyrinthine patterns. The second is a Nonequilibrium Ising-Bloch (NIB) bifurcation that renders a stationary planar front unstable and gives rise to a pair of counterpropagating fronts. Near the NIB bifurcation the relation of the front velocity to curvature is highly nonlinear and transitions between counterpropagating fronts become feasible. Nonuniformly curved fronts may undergo local front transitions that nucleate spiral-vortex pairs. These nucleation events provide the ingredient needed to initiate spot splitting and spiral turbulence. Similar spatio-temporal processes have been observed recently in the ferrocyanide-iodate-sul te reaction.

Dynamic front transitions and spiral-vortex nucleation

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1995

This is a study of front dynamics in reaction di usion systems near Nonequilibrium Ising-Bloch bifurcations. We nd that the relation between front velocity and perturbative factors, such as external elds and curvature, is typically multivalued. This unusual form allows small perturbations to induce dynamic transitions between counter-propagating fronts and nucleate spiral vortices. We use these ndings to propose explanations for a few numerical and experimental observations including spiral breakup driven by advective elds, and spot splitting. 05.45.+b, 82.20Mj

Front dynamics in an oscillatory bistable Belousov-Zhabotinsky chemical reaction

Physical Review E, 2004

We observe breathing front dynamics which select three distinct types of bistable patterns in the 2:1 resonance regime of the periodically forced oscillatory Belousov-Zhabotinsky reaction. We measure the curvaturedriven shrinking of a circular domain R ϳ t 1/2 at forcing frequencies below a specific value, and show that the fast time scale front oscillations (breathing) drive this slow time scale shrinking. Above a specific frequency, we observe fronts of higher curvature grow instead of shrink and labyrinth patterns form. Just below the transition frequency is a relatively narrow range of frequencies where the curvature-driven coarsening is balanced by a competing front interaction, which leads to a pattern of localized structures. The length scale of the localized structure and labyrinth patterns is set by the front interactions.

Chemical Reaction Fronts in Ordered and Disordered Cellular Flows with Opposing Winds

Physical Review Letters, 2008

We present experiments on the motion of chemical fronts in ordered and disordered vortex flows with imposed uniform winds. Fronts in a chain of alternating vortices are found to freeze (pin to the separatrix) for a wide range of opposing winds that grows nonlinearly with the characteristic strength of the underlying vorticity. Experiments in spatially disordered flows demonstrate that freezing of fronts is common to cellular flows; furthermore, it is not dependent on boundary conditions. We therefore anticipate similar pinning in a wide range of 2D cellular flows and front-producing systems.

Pinning and mode-locking of reaction fronts by vortices

Communications in Nonlinear Science and Numerical Simulation, 2011

We present results of experiments on the behavior of reaction fronts in the presence of vortex-dominated flows. The flow is either a single vortex or a chain of vortices in an annular configuration, and the reaction is the excitable Belousov-Zhabotinsky chemical reaction. If the vortex chain oscillates periodically in the lateral direction, the reaction front often mode-locks to the oscillations, propagating an integer number of wavelengths of the flow (two vortices) in an integer number of drive periods. In the presence of a uniform ''wind'', the front often freezes, remaining pinned to the leading vortex and neither propagating forward against the wind nor being blown backward by it. Studies with an individual vortex verify the ability of a moving vortex to pin and drag a reaction front. We use this pinning behavior to explain the mode-locking for the oscillating case.