Time evolution of the energy-injection scale, Lin (thick solid line), computed from the integral of the inverse wave number, 1/k, weighted by the velocity power spectrum, E(k). The time-averaged value of 70.5 pc is shown by the horizontal dashed line. The dotted line shows the rms velocity, σv. Almost all peaks in σv correspond to peaks in Lin. The thin solid line shows the time evolution of the transverse integral scale, L22. The average value, ⟨L22⟩ = 19.4 pc, is shown by the horizontal dashed-dotted line.
Power spectra of velocity, E(k), solenoidal velocity component, Es(k), compressive velocity component, Ec(k), square root of kinetic energy, EK(k), and magnetic field, Em(k), obtained from the average of the power spectra of the x, y and z components of these fields in the root grid (1283 computational cells) of a single snapshot at time t = 52.75 Myr. This time captures the early expansion of a SN remnant to a diameter of approximately 30 pc, as indicated by the peak of the velocity power spectrum. The wavy appearance of Ec(k) is explained in the text. The fact that Es does not show similar fluctuations, and Es < Ec at the energy peak, indicates that this remnant has so far expanded into a relatively uniform hot medium, where the baroclinic effect is negligible and solenoidal modes are not efficiently generated yet.
Power spectra averaged over 66 snapshots within the time interval t = 40.5 − 48.8 Myr. During this time interval the random SN rate is a bit lower than during the first and last third of the simulation, so there is a reduced probability that a snapshot captures the early expansion of SN remnants with the corresponding perturbations to the power spectra. As a result, the time average is representative of the statistically relaxed power spectra. The power-law slopes are obtained from a least-square fit in the range of wave numbers 4.2 ≤ k Lbox/2π ≤ 12.1.
during a SN explosion