Nonlinear dynamical systems and bistability in linearly forced isotropic turbulence  

作　　者：Zheng Ran Xing-Jie Yuan 

机构地区：[1]Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University

出　　处：《Acta Mechanica Sinica》2013年第6期823-826,共4页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(11172162,10572083)

摘　　要：In this paper, we present an extensive study of the linearly forced isotropic turbulence. By using analytical method, we identify two parametric choices, of which they seem to be new as far as our knowledge goes. We prove that the underlying nonlinear dynamical system for linearly forced isotropic turbulence is the general case of a cubic Lienard equation with linear damping. We also discuss a FokkerPlanck approach to this new dynamical system, which is bistable and exhibits two asymmetric and asymptotically stable stationary probability densities.In this paper, we present an extensive study of the linearly forced isotropic turbulence. By using analytical method, we identify two parametric choices, of which they seem to be new as far as our knowledge goes. We prove that the underlying nonlinear dynamical system for linearly forced isotropic turbulence is the general case of a cubic Lienard equation with linear damping. We also discuss a FokkerPlanck approach to this new dynamical system, which is bistable and exhibits two asymmetric and asymptotically stable stationary probability densities.

关 键 词：Isotropic turbulence Nonlinear dynamical system Karman-Howarth equation 

分 类 号：O357.5[理学—流体力学]