A note on a new theory of turbulence

Abstract

In this paper, the creation and annihilation of turbulent eddies are described as elementary particles in the quantum field theory. An elementary particle may be considered as a solid entity as it exists in quantum theory, but a turbulent eddy is often changed in size and shape with time due to its energy dissipation in a turbulent field. Therefore, in order to apply the method of the quantum field theory to the turbulent field by analogy, the entity of the same eddy should be defined firstly. According to the linearized theory, the turbulent eddies with the similarity character in lime duration may he considered as the entity of the same eddy, and the creation and annihilation of turbulent eddies without the similar characters are related to the interaction term φ_i in equation (2.6). Then, the creation operator and annihilation operator similar to those in the quantum field theory are used to describe the state of turbulent eddy field. Finally, a “Schrödinger” equation of turbulent eddies is formulated based upon the nonlinear terms in the original N-S equation. Thus, a new turbulent eddy interaction theory similar to the quantum field theory is obtained.