Origin of universal nonlinear SSD efficiency and duration

Determine the physical explanation for why the nonlinear small-scale dynamo exhibits an efficiency of approximately 1/100 for conversion of hydrodynamic energy flux into magnetic energy and a characteristic nonlinear-phase duration of approximately 20 outer-scale turnover times, rather than different values.

Background

The paper measures the nonlinear growth of magnetic energy in small-scale dynamos across subsonic and supersonic regimes and finds two striking universal features: an energy conversion efficiency of about 1/100 of the turbulent cascade rate and a nonlinear-phase duration of roughly 20 turnover times. These values appear independent of Reynolds number and Mach number in the simulations.

Despite establishing these empirical regularities, the authors note that current theory does not explain why these specific numerical values arise. Understanding the controlling dynamical processes or scaling arguments that select these values is essential for a predictive theory of nonlinear dynamo evolution.