Impact of small scale turbulent flows on dynamo actions

•The integral equation approach is extended to investigate the dynamo actions driven by the turbulent flows.•The results show that the strong isotropic turbulence prefers to excite the m=0m=0 magnetic mode for the dynamo actions.•The weak turbulence may have a detrimental or helpful effect on the dynamo actions, which depends on mean flows.

Based on the mean-field dynamo theory, the integral equation approach is extended to investigate the impact of the small scale turbulence on the onset of the dynamo actions in the cylindrical vessel by taking the Beltrami-like flows as mean flows and modeling the small scale turbulence with α  -effect. The numerical results show that the small scale isotropic turbulence may have a detrimental or helpful effect on the onset of the dynamo action, which depends on the mean flow. However, the strong isotropic turbulence prefers to excite the m=0m=0 magnetic mode.