Floquet stability and Lagrangian statistics of a nonlinear time-dependent ABC dynamo

The Lagrangian statistics of a time-dependent ABC flow are considered, with time dependence introduced via harmonic oscillation with frequency Q. By calculating the finite-time Lyapunov exponents (FTLEs), the Lagrangian statistics of the system are determined for a range of values of Q. These statistics are calculated for the kinematic regime where the flow remains an ABC flow, the nonlinear regime with dynamo action present, and a second hydrodynamic state reached through instability of the original ABC flow. It is found that there are significant differences between these three states, with most cases showing a decrease in their FTLEs as the flow deviates from its original ABC form. Furthermore, these changes are highly dependent on Q, with lower frequencies leading to higher FTLEs in the nonlinear regime, and unstable regimes. By examining the Lagrangian statistics with respect to the dynamo behavior observed, we discuss their potential relevance to nonlinear saturation, self-killing dynamos, and the importance of the initial hydrodynamic state. The numerical code developed for this project is also available.