表示湍流场的一种新设想  

A Note on a New Theory of Turbulence

作　　者：蔡树棠[1] 林多敏 

机构地区：[1]中国科技大学 [2]上海市应用数学和力学所

出　　处：《应用数学和力学》1991年第1期91-95,共5页Applied Mathematics and Mechanics

摘　　要：本文仿照量子场论中描述基本粒子产生湮灭的方法来描述湍流中涡旋的产生和消灭.因为当某一基本粒子存在的时候,我们可以认为它是一个不变实体,而湍流中涡旋则在时间过程中不断变化和耗散,所以在类比应用量子场论方法时首先要解决怎样的湍流涡旋可认为是同一个涡旋.根据线性化理论的特点,我们认为在时间过程中按相似性规律变化时湍流涡旋才算是同一个涡旋,而把不具有相似性的涡旋出现或消失,看成是方程(2.6)中相互作用项φ_i所引起的湮火和产生的结果.然后,我们采用和量子场论相类似的产生算符和消灭算符来描述湍流涡旋系统所处的状态.最后,我们利用原N-S方程中相互作用项来构成涡旋相互作用的“Schr(?)dinger”方程以描述其状态的变化.这样就得类似于量子场论的湍流涡旋相互作用理论.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 time duration may be 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 φi 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 'Schrodinger' 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

关 键 词：湍流 涡旋 相互作用 量子场论 

分 类 号：O357.5[理学—流体力学]