Generalized entropies in a turbulent dynamo simulation

A simulation of hydromagnetic turbulence exhibiting dynamo action is employed to estimate the generalized entropies, ${\mathit{H}}_{\mathit{q}}$, from the distribution of moments of local expansion factors of material line elements. These generalized entropies can be used to characterize the dynamics of turbulence and of nonlinear dynamo action. The value of the metric entropy, ${\mathit{H}}_1$, is comparable to the largest Lyapunov exponent describing the divergence of trajectories in phase space, which in turn is somewhat larger than the growth rate of the magnetic energy. The value of the topological entropy, ${\mathit{H}}_0$, is similar to the conversion rate of kinetic to magnetic energy, but larger than the growth rate of the dynamo. This is in agreement with results stating that the growth rate of the kinematic dynamo is limited by the topological entropy. The dependence of ${\mathit{H}}_{\mathit{q}}$ on q leads to a criterion from which we infer that the degree of intermittency in our particular system is weak.