Towards a complex system approach for the study of turbulence

Turbulence is composed of eddy motions that have excitations over a continuous range of scales and display various spatially localized processes such as turbulence production, diffusion, and dissipation. The complexity of turbulence manifests in both its scale distribution and its complex dependence on physical conditions. We propose a system approach for the study of turbulence that comprises two parts, a scaling analysis that gives rise to a set of local statistical measures for the quantification of the fluctuation state, and a system analysis that determines the spatial variation of scaling over the entire domain of the flow. In this paper, we present the basis for the approach, which is the existence of a hierarchical similarity (HS) property that holds for a variety of turbulent systems. Three systems will be discussed: a mixing layer flow of fluid motions, a chemical reaction system modelled by the complex Ginzburg–Landou equations displaying two-dimensional spiral and chaotic patterns, and DNA sequences that record long-term evolutionary history of biological species. All three systems have a continuous range of fluctuations across scales, and all display the HS property which then holds as the universal principle of the self-organization. It is proposed that the parameters derived from the HS study can be used for the description of local ensemble of turbulent structures, and their spatial variations form a new set of statistical measures of turbulence. Future study involving the measurement of the nonlinear response of the ensemble of eddies to external factors is discussed at the end.