Attractive fixed-point solution study of shell model for homogeneous isotropic turbulence  

作　　者：郭昊 李超 屈秋林 刘沛清 

机构地区：[1]Institute of Fluid Mechanics, Beihang University [2]Key Laboratory of Fluid Mechanics Under the Ministry of Education, Beihang University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2013年第3期259-268,共10页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (No. 10902007);he National Basic Research Program of China (973 Program) (No. 2009CB724001)

摘　　要：The attractive fixed-point solution of a nonlinear cascade model is stud- ied for the homogeneous isotropic turbulence containing a parameter C, introduced by Desnyansky and Novikov. With a traditional constant positive external force added on the first shell equation, it can be found that the attractive fixed-point solution of the model depends on both the parameter C and the external force. Thus, an explicit force is introduced to remove the effects of the external force on the attractive fixed-point solu- tion. F^arthermore, two groups of attractive fixed-point solutions are derived theoretically and studied numerically. One of the groups has the same scaling behavior of the velocity in the whole inertial range and agrees well with those observed by Bell and Nelkin for the nonnegative parameters. The other is found to have different scaling behaviors of the velocity at the odd and even number shells for the negative parameters. This special characteristic may be used to study the anomalous scaling behavior of the turbulence.The attractive fixed-point solution of a nonlinear cascade model is stud- ied for the homogeneous isotropic turbulence containing a parameter C, introduced by Desnyansky and Novikov. With a traditional constant positive external force added on the first shell equation, it can be found that the attractive fixed-point solution of the model depends on both the parameter C and the external force. Thus, an explicit force is introduced to remove the effects of the external force on the attractive fixed-point solu- tion. F^arthermore, two groups of attractive fixed-point solutions are derived theoretically and studied numerically. One of the groups has the same scaling behavior of the velocity in the whole inertial range and agrees well with those observed by Bell and Nelkin for the nonnegative parameters. The other is found to have different scaling behaviors of the velocity at the odd and even number shells for the negative parameters. This special characteristic may be used to study the anomalous scaling behavior of the turbulence.

关 键 词：TURBULENCE shell model attractive fixed-point SCALING 

分 类 号：O357.5[理学—流体力学]