各向同性湍流能量级串中的旋涡分岔机制

充分发展各向同性湍流能量级串和多尺度相互作用一直是湍流理论研究的核心问题.目前,对于该物理过程的完全理解或精确的数学描述缺乏基于第一原理的理论.简要介绍了湍流能量级串的概念、起源、发展历程及面临的挑战问题,着重阐述了目前各种现有描述方法的局限性.基于三维不可压缩流体的Karman-Howarth方程,根据新得到的各向同性湍流尺度演化方程以及在这一方向上的理论进展,证明存在以湍流Taylor微尺度为动力学量的非线性动力系统.根据上述新的理论,可以认为:湍流能量级串由一系列的旋涡非线性分岔过程刻画,呈现Feigenbaum倍周期分岔的途径.

Nature of vortex bifurcation and cascade in isotropic turbulence

The central problem of fully developed turbulence is understanding the energy cascading process and multiscale interaction.Update,there is no deductive theory which leads to a full physical understanding or mathematical formulation.The definition,development,challenge and the corresponding status of turbulence cascade were briefly reviewed.The limitation of present methods were emphasized.Based on the Karman-Howarth equation in 3D incompressible fluid,a new isotropic turbulence scale evolution equation and its related theory progress,the existence of nonlinear dynamic system measured by turbulence Taylor microscale was proven.The present results indicate that the energy cascading process has remarkable similarities with the determinisitic construction rules of the logistic map.The cascade appears as an infinite sequence of period-doubling vortex bifurcations.