Lorenz方程中两种尺度的相互作用

Interaction of two kind scales in Lorenz equation

在Lorenz方程中的混沌区域,存在着两种尺度的相互作用.其中代表大尺度运动的Rayleigh数r决定空气中小尺度的对流和湍流运动,而对流和湍流运动又对大尺度运动具有反馈作用,两者的相互作用最终使r值减小,空气运动进入一种定常状态.在反馈过程中,垂直热通量xy及垂直温度梯度z—的变化是决定r变化的主要原因,并且反馈的最终结果表现出突变的特征.

In the chaos range of Lorenz equation, there is interaction between the smaller and larger scales. On the one hand, the Rayleigh number r determines the convective and turbulent flows in the air. On the other hand, the convective and turbulent flows have a feedback to the larger scale condition. The result of interaction between the scales leads to the decrease of the value of r, until the steady state of Lorenz equations is established. During the feedback process, the variation in vertical thermal flux xy and vertical temperature gradient z are the main causes that decide the change of number r. Moreover the end result of feedback displays a abrupt change.