Gradient vortex dynamics in 3D-weak turbulence.

Vortex dynamics play a central role in most turbulent processes, whether of physical or chemical origin. In the realm of so-called weak turbulence, which encompasses physical, chemical, and electrochemical processes, understanding and monitoring the emergence of vortices in three dimensions remains a significant challenge. In this study, we propose a novel approach with minimal computational cost that enables the characterization of vortex ring formation and screw-like patterns in 3D-turbulent flows. Our method involves analyzing gradient vortex dynamics by measuring phase fluctuations in gradient patterns derived from the 3D-distribution of the corresponding amplitudes. The investigation focuses on transient primary structures generated by the Complex Ginzburg-Landau amplitude equation. The simulations integrate gradient pattern analysis, allowing for a groundbreaking association between phase fluctuations (commonly referred to as phase turbulence) and the helical oscillations induced by vorticity. As our main result, the phase-gradient analysis, combined with aspect ratio measurements of the primary patterns of coherent structures, enables us to identify at least four distinct regimes characterizing vortex dynamics. To further enhance this characterization, spectral measurements and recurrence plots of the phase-gradient fluctuations are introduced as innovative tools for describing weak turbulence and spatiotemporal chaos in nonlinear ([Formula: see text]) dynamics. This approach provides new insights into the intricate interplay between phase turbulence and vortex dynamics, offering a new perspective on the systematic study of the formation of coherent structures in three dimensions. It is worth highlighting that this is the first time that 3D screw dynamics have been simulated, visualized and analyzed in detail in a phase turbulence process.