与えられたパワースペクトルとクロススペクトルをもつ多次元風速変動のシミュレーションとその精度の検討

抄録

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 A_s and A_c 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 A_s and A_c 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 A_s and A_c 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 A_s and A_c 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.