Probing quasigeostrophic turbulence via complex networks

Using statistical analysis and complex networks, we study the role of inverse Rossby deformation radius, λ, on freely decaying quasi-geostrophic turbulence dynamics. We find that the area fraction occupied by vortices remains constant over an extended duration for all values of λ. We establish an energy spectrum scaling based on a self-similar distribution of vortices of area, A, during this period. Our findings suggest that the vortex number density follows the relationship n(A)∼N_vA^-p, and the inertial range energy spectra scales as k^-7+2p, where N_v represents the number of vortices, k is the wavenumber and p depends on λ. To investigate vortical interactions, we construct a spatiotemporal weighted network. Our analysis uncovers two distinct strength distributions: (1) a briefly observed scale-free distribution resulting from nonlocal interactions when λ<0, and (2) a truncated scale-free distribution due to local interactions over an extended period when λ>>k₀, where k₀ denotes the initial characteristic wave number at which the total energy is at its maximum. Both networks are robust against random disturbances but are vulnerable to targeted attacks on their hubs. Additionally, we found that these network hubs contribute to the large-scale energy spectra, which can be reconstructed using only 1% of the total degrees of freedom in a quasi-geostrophic turbulent field.