Direct Numerical Simulation of Mechanically Driven Turbulent Dynamos in Spherical Geometry

A parallel version of a nonlinear pseudo-spectral MHD code for the simulation of liquid metal dynamos in spherical geometry was developed using a domain decomposition technique. The parallel code exhibits ideal scaling going up to 8 CPUs on shared-memory machines. At 16 CPUs, it still achieves efficient speedups between $14$ and nearly $16$. Given today's computational speed, it is now possible to resolve fluid Reynolds numbers of $\mathrm{Re} \approx 4000$ in the simulations, whereas previous serial computations were limited to $\mathrm{Re} \approx 1500$. Direct numerical simulations are performed to explore the dynamo threshold $\mathrm{Rm_{crit}}$ (the critical magnetic Reynolds number) in $\mathrm{Re}$-$\mathrm{Rm}$-space for the flow profile of the Madison Dynamo Experiment. The shape of $\mathrm{Rm_{crit}}$ has been determined up to $\mathrm{Re} \approx 3000$. Furthermore, the code was adapted to model the driving of a new generation of dynamo experiment using plasma instead of liquid metal. By employing pure toroidal driving in two thin counter-rotating hemispherical shells along the walls, numerical simulations show that the system reaches a quasi-stationary state with a self-excited magnetic field.