Characterizing Space-Time Chaos in an Experiment of Thermal Convection

Abstract

In the last decade, dynamical system theory has provided several tools to analyse quantitatively the transition to low dimensional chaos¹ observed in many experiments². In contrast a general characterization of spatiotemporal chaos is still an unsolved problem, that has recently received a lot of interest both from a theoretical ^3–10 and experimental point of view^11–13. In fluid dynamics the main goal of this research is to understand the relationship between chaos and the turbulent regimes, where the fluid motion presents a chaotic evolution both in space and time. Indeed in spatially extended systems, such as a fluid, the transition to low dimensional chaos is associated with relevant spatial effects, but the unpredictable time evolution does not influence the spatial order. In other words the correlation length is comparable with the size of the system. So, in order to give more insight into the problem of the transition to turbulence it is very important to study the role of the spatial degrees of freedom in temporal chaotic regimes and the reasons why the spatial coherence is lost. The simplest mathematical models, in which the features of the transition to spatiotemporal chaos may be analysed, are systems of coupled maps^4–6, one dimensional partial differential equations^3,6,7,8 and cellular automata⁹. One of the typical regimes, presented by these models, is spatiotemporal intermittency,that consists of a fluctuating mixture of laminar and turbulent domains with well defined boundaries. Such a phenomenon has a physical relevance because it is similar to those observed in Rayleigh-Benard convection ^13,14 and in boundary layer flows ¹⁵