强非线性湍流的不稳定性分析

为了应用拟态动力学(fractal dynamics)概念分析湍流不稳定性,选择带有离散扰波的任意曲线作为湍流拟态结构基元。在基元上建立量级化的尺度与坐标系,用以分析有复杂结构的湍流强非线性问题,湍流分析中的非线性及离散性二大难题得到了解决。所得通向转捩与湍流的分叉解,全面反映强非线性和离散性的效应,即剪切、拉伸、旋转、弥散、压力与变形相互作用及记忆诸因素对不稳定性的影响。本文有助于加深对湍流基本物理特性的理解。

INSTABILITY ANALYSIS OF STRONG NONLINEARITY OF TURBULENT FLOW

In order to analyse the instability of turbulent flow from the viewpoint of fractal dynamics, an arbitrary curve with discrete disturbance wave is chosen as the element of fractal structures of turbulence. Meanwhile, a quantized scale and coordinate method is adopted to handle the strongly nonlinear phenomena of flows despite their complex structures and large amplitudes of disturbance. Two of the main difficulties for the complexity of turbulence,i.e. nonlinearity and discreteness, have been approximately solved by the above-mentioned means. The bifurcated solution leading to transition and turbulence is meaningful, which embraces all the effects of nonlinearity and discreteness, including shearing, stretching, rotation, dispersion, pressure-strain interaction and memory. Therefore, the result should deepen our comprehension of turbulence.