Effect of quenching of horizontal motions by strong magnetic field. We show the relation of the quenched Poynting flux as defined in Eq. (A.5) to the unsigned surface magnetic flux Φ. Each data point represents an average in time and space for each run. The values are normalized to model run 1B represented here by the subscript ‘ref’. The black line shows the power-law fit to the case where no quenching is included (i.e. q_sat = 1). The red and blue lines show power-law fits for q_sat = 2∕3 and 1/3. The corresponding power-law indices β for are given with the legend.