Table 1
Key properties of Aδ(k) for the simulated models: normalization (maximum), slope, and scale of significant decay.
| Mach ~ 0.25 | Mach ~ 0.5 | Mach ~ 0.75 | Mach ~ 0.25, L/2 | |
|
|
||||
| Aδ(k) normalization | ||||
| f = 0 (hydro) | 6.4% | 11.7% | 18.8% | 5.3% |
| f = 10-3 | 6.4% | 11.7% | 18.8% | 5.1% |
| f = 10-2 | 6.0% | 11.3% | 18.6% | 4.8% |
| f = 10-1 | 4.6% | 10.0 % | 16.8% | 3.5% |
| f = 1 | 3.2% | 9.1 % | 15.4% | 3.3% |
|
|
||||
| Aδ(k) slopea | ||||
| f = 0 (hydro) | −1/3 | −1/5 | −1/5 | −1/5 |
| f = 10-3 | −1/3 →b −1/2 | −1/5 →b −1/2 | −1/5 →b −1/2 | −1/2 |
| f = 10-2 | −1/2 →b −4/5 | −1/3 →b −1/2 | −1/3 →b −1/2 | −1/2 |
| f = 10-1 | −2/3 | −4/9 | −4/9 | −4/9 |
| f = 1 | −1/2 | −4/9 | −4/9 | −4/9 |
|
|
||||
| Aδ(k) decay | ||||
| f = 0 (hydro) | × | × | × | × |
| f = 10-3 | 100 kpc | 60 kpc | 45 kpc | 60 kpc |
| f = 10-2 | ~L | 330 kpc | 240 kpc | ~L′ = L/2 |
| f = 10-1 | > Lb | > Lb | > Lb | > L′b |
| f = 1 | > Lb | > Lb | > Lb | > L′b |
Notes.
The energy and power spectrum slopes are retrieved through 
and 
. For instance, the A(k)δ slopes −1/3 and −1/2 correspond to the classic Kolmogorov and Burgers energy slopes −5/3 and −2, commonly observed for the velocity energy spectrum.
Models with strong conduction (f ≳ 0.1) produce a suppression of δ perturbations over the whole range of scales, inducing a decrease in normalization. The A(k)δ decay occurs near Pt ~ 100. Notice that the decay is not a sharp cutoff, due to the continuous turbulent regeneration. This is characterized by an exponentially changing slope, especially in the models with f ≲ 10-2 (denoted with the → symbol).
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