Dynamical Complex Network Models of the Turbulent Cascade

Cascade models based on dynamical complex networks are proposed as models of turbulent energy cascade. Taking a simple shell model as the initial regular lattice with only nearest neighbor interactions, small world network models are constructed by adding or replacing some of the existing local interactions by nonlocal ones. The models are then evolved over time, both by solving for the shell variable for velocity using an arbitrary network generalization of the shell model evolution and by rewiring the network each time from the original lattice in regular time intervals. This results in a more intermittent time evolution with larger variations of the wave-number spectrum. It also results in an actual increase in intermittency as computed from the fitted exponents of structure functions as computed from these models. It appears that the intermittency increases as the ratio of random nonlocal connections to local nearest neighbor connections increases.