脉动风速随机Fourier波数谱研究

Research on Stochastic Fourier Wavenumber Spectrum of Fluctuating Wind Speed

摘要:

从物理机制出发,建立了具有扎实物理基础的脉动风速随机Fourier谱模型.首先,基于大气湍流物理图景,阐述了湍流中的涡旋尺度和风速能谱不同子区的对应关系.以脉动风速在剪切含能子区和惯性子区所符合的不同幂次规律为基础,建立了随机Fourier谱模型,指出上述两个子区分界波长lc对应实际物理过程中含能大涡尺度和平衡范围涡旋尺度的分界值.本质上,lc是一个随机变量,影响lc的主要因素是湍流涡量和剪切率的比值.利用实测数据,建立了lc和剪切率以及Fourier谱模型中各参数的关系.最后,以地面粗糙度和10 min平均风速为基本随机变量,湍流强度为牵连随机变量,得到了分界波长的分布以及以双线性函数为特征的随机Fourier波数谱.理论预测结果和实际观测结果符合良好.

Abstract:

Based on physical mechanism,a stochastic Fourier spectrum model of fluctuating wind speed with solid physical basis is proposed.In view of physical scene of atmospheric turbulence,relationship between the scales of vortex in turbulence and the subranges in energy spectrum is revealed.According to the exponential laws of Fourier spectrum in different energy ranges,a stochastic Fourier spectrum model is established.In actual physical process,the boundary wavelength lc of the two subranges corresponds to the boundary value of the scales of vortexes in energycontent range and in equilibrium range.Essentially,lcis a variable and the main physical factor which affects its value is the ratio between shearratio of the mainflow and vorticity of turbulence.It is found that the ratio is proportional to shearratio.Along with numerical calculation,the formula to calculate lc and the other parameters in Fourier spectrum model is founded.Finally,taking ground roughness length and 10 min mean wind speed as two basic variables and turbulence intensity as related variable,the distribution of lc and the normalized stochastic Fourier wavenumber spectrum with the bilinear characteristic can be obtained.The theoretical results accord with the measured results well.