Dynamical network models of the turbulent cascade

Abstract

Cascade models based on dynamical complex networks are proposed as models of the 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 velocity variable 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 wavenumber spectrum. It also results in an increase in intermittency, computed from the exponents of structure functions obtained from these models. It is observed that the intermittency increases as the ratio of random nonlocal connections to local nearest-neighbor connections increases. The possibility of extraction of such models from direct numerical simulations is discussed and a detailed example for two dimensional turbulence is given.