Bifurcations in reaction-diffusion systems in chaotic flows.
نویسندگان
چکیده
We study the behavior of reacting tracers in a chaotic flow. In particular, we look at an autocatalytic reaction and at a bistable system which are subjected to stirring by a chaotic flow. The impact of the chaotic advection is described by a one-dimensional phenomenological model. We use a nonperturbative technique to describe the behavior near a saddle node bifurcation. We also find an approximation of the solution far away from the bifurcation point. The results are confirmed by numerical simulations and show good agreement.
منابع مشابه
Optimal Stretching in Advection-Reaction-Diffusion Systems.
We investigate growth of the excitable Belousov-Zhabotinsky reaction in chaotic, time-varying flows. In slow flows, reacted regions tend to lie near vortex edges, whereas fast flows restrict reacted regions to vortex cores. We show that reacted regions travel toward vortex centers faster as flow speed increases, but nonreactive scalars do not. For either slow or fast flows, reaction is promoted...
متن کاملPeriodic Orbits and Chaotic Sets in a Low-Dimensional Model for Shear Flows
Abstract. We consider the dynamics of a low-dimensional model for turbulent shear flows. The model is based on Fourier modes and describes sinusoidal shear flow, in which fluid between two free-slip walls experiences a sinusoidal body force. The model contains nine modes, most of which have a direct hydrodynamical interpretation. We analyze the stationary states and periodic orbits for the mode...
متن کاملOscillatory and chaotic dynamics in compartmentalized geometries.
The effects of spatial compartmentalization of a multistep reaction mechanism (Willamowski-Rössler model) whose mass action rate law shows oscillations and chaotic dynamics are explored. The mechanism is decomposed into subsets of reactions that are then assumed to take place in distinct regularly or randomly distributed spatial domains in the system. The reactive domains are coupled by diffusi...
متن کاملTemporal chaos versus spatial mixing in reaction-advection-diffusion systems.
We develop a theory describing the transition to a spatially homogeneous regime in a mixing flow with a chaotic in time reaction. The transverse Lyapunov exponent governing the stability of the homogeneous state can be represented as a combination of Lyapunov exponents for spatial mixing and temporal chaos. This representation, being exact for time-independent flows and equal Pe clet numbers of...
متن کاملExperimental studies of front propagation and mode-locking in an advection-reaction-diffusion system
– Experiments are presented on reaction processes in a cellular, time-periodic fluid flow composed of a chain of oscillating vortices. Previous studies have shown that mixing of passive impurities in this flow is chaotic. Chemical fronts are studied in this flow using the excitable regime of the ruthenium-catalyzed Belousov-Zhabotinsky reaction. The velocities of the fronts are measured as a fu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 71 6 Pt 2 شماره
صفحات -
تاریخ انتشار 2005