Fig. 6
Outputs from the analysis of weak turbulence dynamics simulated with (\(3D+1\))-CGLE. Up: Variation of the aspect ratio, \(\Gamma _{\ell }\), over time. Average values are presented for each set of 25 snapshots making up 40 representative measurements. The bias range is represented by the variation in standard deviation over time. Four main regimes are identified and separated by black dotted lines. The identification of the four regimes, in a \(32\times 32\times 32\) simulation, was the main result that validated this simulation for the analysis of the phase-gradient. The translucent violet bands identify the occurrence of the main screws (the most striking of them with \(\Gamma _{\ell } \approx 0.65\) (s465) shown in detail in Fig. 8). Bottom: Values of \(G_{\phi }\) calculated for each gradient hypercube. The result shows that the typical oscillations of vortex dynamics begin during regime II. Until approximately the end of regime III there is greater instability (orange translucent band) until the beginning of regime IV which imposes a decrease in the peak of the oscillations resulting in greater stability of the phases without the presence of asymmetries imposed by thinner vortexes. The values of \(G_{\phi }\) fluctuate as more pairs of symmetric vectors are disregarded from the calculation of \(G_{\phi }\). Table 2 presents representative average values for the main emerging patterns identified in this study. In the inset, the average frequency of the vortex dynamics represented by the fluctuation of \(G_{\phi }\) was obtained with the Fast Fourier Transform (FFT), resulting in 0.38Hz for 30 seconds of observation taking only the oscillation band (colored part of the time series that starts at time-step=247).
