| Paper description |
In this paper, a novel multi-dimensional complex non-equilibrium phase transition model
is put forward to describe quantitatively the physical development process of turbulence
and develop the Kolmogorov turbulence theory from the catastrophe theory, in which the
well-known −5/3 power law is only a special case in this paper proving the accuracy of
our methods. Catastrophe theory is a highly generalized mathematical tool that summarizes the laws of non-equilibrium phase transition. Every control variable in catastrophe
theory could be skillfully expanded into multi-parameter multiplication with different
indices and the relationship among these characteristic indices can be determined by
dimensionless analysis. Thus, the state variables can be expressed quantitatively with
multiple parameters, and the multi-dimensional non-equilibrium phase transition theory
is established. As an example, by adopting the folding catastrophe model, we strictly
derive out the quantitative relationship between energy and wave number with respect
to a new scale index α to quantitative study the whole process of the laminar flow to
turbulence, in which α varies from −2 to −6=5 corresponding to energy containing range
and α = −9=5 to energy containing scale where −10=9 power law is deduced, and at
α = −6=5 the −5=3 law of Kolmogorov turbulence theory is obtained, and fully developed turbulence phase starts at α = −2=3 giving −3 law. Furthermore, this theory
presented is verified by our wind tunnel experiments. This novel non-equilibrium phase
transition methods cannot only provide a new insight into the turbulence model, but
also be applied to other non-equilibrium phase transitions. |
(创新港)
