Simulation of multidimensional wind fluctuations associated with given power spectra and cross spectra and its accuracy
Simulation of multidimensional wind fluctuations associated with given power spectra and cross spectra and its accuracy
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给定功率谱和交叉谱的多维风脉动模拟及其精度
DOI：
10.5359/jawe.1988.36_11
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发表时间：
1988
期刊：
影响因子：
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通讯作者：
Y. Iwatani
中科院分区：
文献类型：
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作者：
Y. Iwatani
前文讨论了一种利用计算机模拟具有特定功率谱和交叉谱的多维风波动的方法。该方法基于多维自回归过程。本文讨论了模拟的精度问题，模拟的风功率谱和交叉谱都可以从常系数矩阵A(γ)(γ=1，2，…)中得到，M)的多维自回归表达式和元素为随机变量的方差和协方差的矩阵D。这些功率谱和交叉谱不存在有限长度时间序列的谱分析引起的模糊性。相应地，我们可以通过将这些谱与模型的谱进行比较来准确地检验模拟的精度，模拟的精度由参数As和Ac定义。当湍流结构模型(功率谱、交叉谱、风波动序列的个数κ、时间间隔Δt、模拟风波动的邻近点之间的距离ΔL等)已经确定，只有离散傅里叶逆变换的L项数和多维自回归过程的阶数M才影响模拟的精度。一般来说，当L的震级大于M的震级时，精度会有所提高。精度不仅受功率谱和交叉谱的形状的影响，而且还受参数κ，Δt、ΔL等人的影响。本文讨论了在湍流风场测量的基础上对一个模式模拟的精度As和Ac，主要讨论了As和Ac随L和M的变化情况，如κ，Δt，ΔL等人对各种参数的取值，如ΔL小于0.2 S(几乎等于对数功率谱峰值周期的1/160)，很难获得1%以上的精度。对于1s的时间间隔Δt，可以进行高精度的模拟。时间间隔对精度有很大的影响。精度随其他参数的变化而变化，精度As和Ac随各种参数的变化如图5至14和表1所示。这些结果不可能推广到其他模型。因此，如有必要，应使用上述方法获得每个模型的精度。
A method by which multidimensional wind fluctuations with specified power spectra and cross spectra could be simulated with the aid of a computer was discussed in the previous report. The method was based on the multidimensional autoregressive process. In the present paper we deal with an accuracy of the simulation.The power spectra and the cross spectra of the simulated winds can be obtained from both the constant coefficient matrix A (γ) (γ=1, 2, …, M) of the multidimensional autoregressive expression and the matrix D whose elements are the variances and the covariances of random variables. These power spectra and cross spectra are free from the ambiguity caused by the spectral analysis of the finite length of time series. Accordingly, we can test exactly the accuracy of the simulation by comparing these spectra with those of the model, The accuracy of the simulation was defined by the parameter As and Ac as shown in the text.When a model of turbulent structures (power spectra, cross spectra, the number κ of the series of wind fluctuations, the time interval Δt, the distance Δl between neighboring points where the wind fluctuations are simulated et al.) has been specified, only the number L of terms of the descrete inverse Fourier transform and the order M of multidimensional autoregressive process influence upon the accuracy of the simulation. Generally speaking, the accuracy is improved when we make the magnitude of L larger than that of M.The accuracy is influenced by not only the shapes of power spectra and cross spectra but also the magnitudes of parameters κ, Δt, Δl et al. We discussed the accuracy As and Ac in the case of the simulation for a model specified on the bases of the measurements of turbulent winds, The discussions were mainly made on the variations of As and Ac with L and M for the various values of parameters κ, Δt, Δl et al, For instance, it is difficult to obtain the accuracy better than 1% for the time interval Δl less than 0.2 s (nearly equal to 1/160 of the period for the peak of the logarithmic power spectra). For the time interval Δt of 1s, it is possible to make the simulation with a high accuracy. The time interval has a large influence upon the accuracy. The accuracy varies with other parameters also The variations of accuracy As and Ac with the various parameters are shown by Figs. 5 to 14 and Table 1. These results are impossible to be generalized for the other models. So, if necessary, the accuracy should be obtained for each model using the method mensioned above.