Lyapunov exponents for hydromagnetic convection

We estimate the two largest Lyapunov exponents in a three-dimensional simulation of hydromagnetic convection in which there is dynamo action. It turns out that these first two exponents (from a total of 8×${63}^3$) are positive and of similar magnitude. Thus we conclude that the dynamo is chaotic. Furthermore, the consideration of local exponents helps in our understanding of the relevant dynamics. We find that the downdraft flows are more chaotic than the upward motions. Likewise, the velocity and magnetic fields have more chaotic dynamics than the temperature and density fields.