Left plots: radial positions of the top and bottom boundaries as functions of multiples of the respective convective turnover times. The radial position is the average position over all angles, the shading marks the corresponding spatial standard deviation of the boundary position. The white dashed lines indicate the time frame considered to obtain the data for the right column. Thick red lines show the evolution of simulations with a grid size of 360 × 240² cells for comparison. The scales of the y-axis for the top and bottom boundary have been adapted for better visibility. All simulations apply the AUSM⁺-up scheme while the nuclear energy release is boosted by factors of 3 × 10³, 1 × 10⁴, and 3 × 10⁴. Right plot: ratio of entrainment velocity v_e and rms velocity v_rms as a function of the bulk Richardson number Ri_B for the simulations shown in the left column. The horizontal error bars indicate the standard deviations of the temporal means of Ri_B. Vertical error bars correspond to the standard deviations of the entrainment velocities for a sliding window of size ΔN_τconv = 1. The time frame is large enough to filter out sound waves but it is somewhat arbitrary. However, the error bars give an idea of the spread in the entrainment velocity. Markers that are crossed are not considered for fitting Eq. (17) to the data. The fit is shown as solid blue line. The dashed line at high Ri_B marks the regime of extrapolation.