Multiplicity in an optimised kinematic dynamo

Abstract

Multiplicity in optimal kinematic dynamos exists for certain types of symmetry classes and boundary conditions, at least near the lowest dynamo onset . Here we investigate the NNT type dynamo generated by steady flows with impermeable boundary conditions in a cube, where the letter N or T stands for pseudo-vacuum or superconducting boundary conditions along x, y, z directions, respectively. We find the top two of the three branches in the neighbourhood of have their growth rates crossed over at . Within each branch, the spatial structure of the optimal velocity field gradually shifts with respect to . At about above , the original optimal branch has developed distinct combinations of dominant Fourier modes. In contrast, the first suboptimal branch shows the least change in structure. We then follow the evolution of selected optimised solutions when varies until it becomes unstable. Specific modes in the flow that can destabilise the dynamo are identified. Within the range surveyed, we find that there can be one to two dynamo windows. All three branches generate a steady dynamo near , but the first suboptimal branch can generate an oscillatory dynamo at about eight times , and for both suboptimal branches, the growth rate reaches saturation approximately at . We find the two suboptimal branches create a more robust dynamo action supercritically.