Chemical-wave dynamics in a vertically oscillating ﬂuid layer G. Fernández-García, D. I. Roncaglia, * V. Pérez-Villar, A. P. Muñuzuri, and V. Pérez-Muñuzuri † Group of Nonlinear Physics, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain Received 7 May 2007; revised manuscript received 9 October 2007; published 8 February 2008 Classical Faraday experiments were conducted on the oscillatory chemical Belousov-Zhabotinsky BZ reaction. The vertical periodic modulation of the acceleration induces ﬂows in the system that change the BZ dynamics, and thus the patterns exhibited. The resulting reaction-diffusion-advection system exhibits four different types of pattern for increasing stirring amplitude: deformed targets and spiral waves, ﬁlamentary patterns arranged in large-scale vortices, advection phase waves, and ﬁnally front annihilation where the medium becomes homogeneous. A wave period analysis of the forced system has been carried out. Contrary to what is expected, i.e., a continuous increase of the wave period with increasing forcing, the period changes dramatically at the boundaries between pattern domains. DOI: 10.1103/PhysRevE.77.026204 PACS numbers: 82.40.Bj, 47.54.-r, 47.70.Fw, 82.40.Ck I. INTRODUCTION The formation of spatiotemporal patterns in active media due to the interplay between transport processes and auto- catalytic reactions—a ubiquitous phenomenon in nature—is of great relevance to biology, chemistry, etc. 1,2. In many cases of interest, the reaction-diffusion RD dynamics take place in a ﬂuid environment, capable of undergoing a turbu- lent ﬂow. A host of interesting and little-studied phenomena can be expected from the interplay between mixing and RD dynamics. Their study is important to understanding the dy- namics of environmental systems such as plankton popula- tions in the sea 3,4, pollutants in the atmosphere 5,6, and the depletion of the ozone layer 7,8. A closely related prob- lem that has been numerically studied recently is the role of ﬂuid convection in preexisting RD patterns 9–11; the for- mation of patterns in an active medium stirred by chaotic advection has been studied both numerically 12–15 and experimentally 16–18. Under some circumstances, these ﬂows share the property of displaying coherent structures, i.e., well-deﬁned persisting space-time patterns whose posi- tions and shapes may vary randomly 19–21. The inhomo- geneous distribution of the activating and inhibiting species in the presence of these vortices may drastically change the dynamics of the reaction. Because of their relevance for natural processes, it is im- portant to identify those cases where the dynamics of active media advected by a ﬂow may be accessible to laboratory experiments. One such case arises when a ﬂow is created through parametric surface excitation. The Faraday experiment—namely, the generation of surface waves on a ﬂuid subjected to purely vertical vibrations—has been exten- sively studied and has become a model system for pattern formation in hydrodynamic systems 22,23. In the present work we perform experiments based on the forcing of a Belousov-Zhabotinsky BZ reaction 1 by Faraday waves. The resulting reaction-diffusion-advection system exhibits four regions with increasing stirring amplitude: a phase dominated by targets and spiral patterns deformed by the advection ﬂow, ﬁlamentary structures organized into vortical structures, synchronized oscillations in the form of reaction- diffusion-advection phase waves, and ﬁnally a homogeneous region where no perturbations in the active media were ob- served. II. EXPERIMENTAL SETUP Figure 1 shows a schematic diagram of the experimental setup. Experiments were performed using an electromagnetic shaker TIRAvib S511, TIRA GmbH connected to a power ampliﬁer TIRAvib BAA 120, TIRA GmbH. The shaker supplies a 75 N sine rated peak force, a maximum accelera- tion of 50g, a maximum rated travel of 10 mm, and a clean frequency range from 2 to 7000 Hz, as speciﬁed by the manufacturer. The drive signal for the power ampliﬁer is * Permanent address: Departamento de Ciencia y Tecnología, Uni- versidad Nacional de Quilmes. Saenz Peña 352 B1876BXD Ber- nal, Buenos Aires. Argentina. † Corresponding author. vicente.perez@cesga.es SHAKER A C FG O CA Am F CCD L DVD PC L Argon BZ FIG. 1. Color online Experimental setup. C is the container, FG the function generator, Am the ampliﬁer, CA the current condi- tioner, A the accelerometer, O the oscilloscope, F the interference ﬁlter 460 nm, PC the personal computer, DVD the digital video device, and L the lamps. Experiments were conducted under an atmosphere of argon. PHYSICAL REVIEW E 77, 026204 2008 1539-3755/2008/772/0262045 ©2008 The American Physical Society 026204-1