The mechanism that generates chaotic pattern dynamics is phase diffusion coupled with a ramp-induced Eckhaus instability. We have also documented several other interesting regimes in Taylor-Couette flow with hourglass geometry that merit additional study. There is also a highly turbulent regime that still exhibits persistent pattern dynamics involving phase slips. Recently we have successfully implemented a control of chaos algorithm on the chaotic pattern dynamics that we previously discovered in Taylor-Couette flow with hourglass geometry. The key idea of the OGY method is to stabilize one of the many unstable periodic motions that underlie a dynamical system's chaotic attractor.
Stabilization is achieved by small perturbations to an accessible system parameter.
The varying strength of the perturbations is determined by a feedback loop that incorporates real-time sampling of the system's dynamics. This method is applicable to highly dissipative systems that are adequately modeled by iterative maps of a single variable. For our single variable we used the time interval between phase slips. Nonetheless, we found that by a simple sorting of the spatial behavior of the pattern, it is possible to untangle the temporal dynamics of the phase slips so that RPF is applicable. In the absence of control perturbations, the time interval varies between 75 and 140 periods of revolution.