A quantitative nonequilibrium phase transition theory for analyzing the turbulence development process

Abstract

In this paper, a quantitative nonequilibrium multi-dimensional phase transition theory is proposed for describing the turbulence spectrum (energy E with wave number k and scaling index [Formula: see text]) of the turbulence development process by a fold catastrophe model. Each of the control variables in this catastrophe model is subtly expressed into a relative multi-parameter multiplication, and then the state variable can be quantitatively described by these parameters. By using this nonequilibrium phase transition theory, the quantitative relationship in the process of turbulence formation can be strictly derived through dimensionless analysis. Therefore, the turbulence development process can be described with respect to a scaling index [Formula: see text], in which there exists an energy containing range with −1.12 power law (E [Formula: see text] k[Formula: see text]) when [Formula: see text] varies from −2 to −1.2, and an inertial subrange with −1.69 power law (E [Formula: see text] k[Formula: see text]) that is almost identical with the famous Kolmogorov’s −5/3 power law when [Formula: see text] varies from −1.2 to −0.8, and then the dissipation range with −2.52 power law (E [Formula: see text] k[Formula: see text]) when [Formula: see text] varies from −0.8 to 0. Furthermore, this quantitative nonequilibrium phase transition theory has been verified by the corresponding theoretical comparison and experiment. This theory provides not only a new understanding of turbulence, but also a new perspective for other complex nonequilibrium phase transitions.