Characterization of period-doubling scenarios in Taylor-Couette flow

The Taylor-Couette system is an extraordinary hydrodynamic system, showing almost all low-dimensional scenarios for routes to chaos for proper boundary conditions. For a period-doubling route to chaos, bifurcation diagrams were experimentally recorded and the dynamic variables such as fractal dimensions, Lyapunov exponents, and entropies are estimated as a function of Reynolds number. The evolution of the correlation dimension ${\mathit{D}}_2$ with Reynolds number Re shows that ${\mathit{D}}_2$∝(Re-${\mathrm{Re}}_{\mathit{c}}$ ${)}^{1/4}$, which is similar to continuous phase transitions. An investigation of the critical phenomena must be performed as high-precision hydrodynamic experiments because the results show that the kind of scenario depends sensitively on the boundary conditions.