The generation of spatio-temporal chaos in large aspect ratio hydrodynamics

Publisher Website
Google Scholar
Abstract
By studying typical hydrodynamic systems in the large aspect ratio limit, the authors show that spatio-temporal chaos is a natural consequence of the availability of secondary hydrodynamic instabilities. The study of such systems beyond the onset of secondary instabilities shows that, within perturbation theory, there exist stationary, spatially biperiodic solutions. Going beyond perturbation theory, it is found that a KAM mechanism is responsible for creating stationary, spatially chaotic solutions. Second, these solutions are shown to have stable and unstable manifolds in function space. They therefore conjecture that, typically, the time evolution is attracted to one of these spatially chaotic states and is then repelled along an unstable direction. In this second stage, topological defects are created if the system is sufficiently wide and couples to two-dimensional modes. Thus, they identify spatio-temporal chaos with a mechanism of generating a random array of defects in an already spatially disordered system.