Development of a multi-layer network model for characterizing energy cascade behavior on turbulent mixing

Abstract

Eddies of various sizes are visible to the naked eye in turbulent flow. Each eddy scale corresponds to a fraction of the total energy released by the turbulence cascade. Understanding the dynamic mechanism of the energy cascade is crucial to the study of turbulent mixing. In this paper, an energy cascade multi-layer network (ECMN) based on the complex network algorithm is proposed to investigate the spatio-temporal evolution of the energy cascade, covering both the inertial and dispersive ranges. The dynamic process of energy cascade is transformed into a topological structure based on the node definition and edge determination. The topological structure allows for the exploration of eddies interaction and chaotic energy transfer across scales. The model results show the intermittent and non-uniform nature of the energy cascade. Meanwhile, the scale gap found in the model verifies the fractal property of the energy evolution. We also found that scales of the generated eddies in energy cascade process are stochastic, and a synchronous energy cascade pattern is demonstrated according to the constructed framework. Furthermore, it provides a topological way to evaluate the contribution of large and small scale eddies. In addition, a network structure coefficient κ is proposed to evaluate the energy transfer strength. It agrees very well with the fluctuation of dissipation rates. All of this shows that the network model can effectively reveal the inhomogeneous properties of the energy cascade and quantify the turbulent mixing intensity based on the intermittent scale interaction. This also provides new insights into the study of fractal scales of nonlinear complex systems and the bridging of chaotic dynamics with topological frameworks.