Simulations of nonhelical hydromagnetic turbulence

Nonhelical hydromagnetic forced turbulence is investigated using large scale simulations on up to $256$ processors and ${1024}^3$ mesh points. The magnetic Prandtl number is varied between 1∕8 and 30, although in most cases it is unity. When the magnetic Reynolds number is based on the inverse forcing wave number, the critical value for dynamo action is shown to be around 35 for magnetic Prandtl number of unity. For small magnetic Prandtl numbers we find the critical magnetic Reynolds number to increase with decreasing magnetic Prandtl number. The Kazantsev $k^{3∕2}$ spectrum for magnetic energy is confirmed for the kinematic regime, i.e., when nonlinear effects are still unimportant and when the magnetic Prandtl number is unity. In the nonlinear regime, the energy budget converges for large Reynolds numbers (around 1000) such that for our parameters about $70\%$ is in kinetic energy and about $30\%$ is in magnetic energy. The energy dissipation rates are converged to $30\%$ viscous dissipation and $70\%$ resistive dissipation. Second-order structure functions of the Elsasser variables give evidence for a $k^{-5∕3}$ spectrum. Nevertheless, the three-dimensional spectrum is close to $k^{-3∕2}$, but we argue that this is due to the bottleneck effect. The bottleneck effect is shown to be equally strong both for magnetic and nonmagnetic turbulence, but it is far weaker in one-dimensional spectra that are normally studied in laboratory turbulence. Structure function exponents for other orders are well described by the She-Leveque formula, but the velocity field is significantly less intermittent and the magnetic field is more intermittent than the Elsasser variables.