Yamaguchi T, Kikkawa S, Parker K H
J Biomech. 1984;17(12):889-95. doi: 10.1016/0021-9290(84)90002-2.
Two types of unsteadiness must be considered when spectral analysis is applied to unsteady turbulence such as that found in the aorta. Firstly, the statistical properties of the turbulence itself change in time and so the definition of spectral density must be reconsidered. Secondly, the turbulent velocity fluctuations, whether they are steady or unsteady, are carried by an unsteady convective velocity which alters their properties as seen by a stationary observer. In the present study, unsteadiness of turbulence in the latter sense is discussed by applying Taylor's hypothesis of 'frozen turbulence' to turbulence with an unsteady convective velocity. If both a 'frozen' pattern of turbulence and a constant convective velocity are assumed, measured frequency spectra can be easily transformed into wavenumber (spatial) spectra, usually as a trivial part of normalisation. In the case of unsteady turbulence, however, the convection velocity is no longer constant and the conventional method can not be used. A new method of estimating the spatial properties of unsteady turbulence is proposed in which the temporal fluctuations of the turbulent velocity are transformed into spatial fluctuations using a nonlinear transformation based upon the unsteady convective velocity. The transformed data are then Fourier analysed to yield a wavenumber spectrum directly. The proposed method is applied to data obtained in the canine ascending aorta. Spectra calculated by the proposed method differ significantly from those obtained by the conventional method, particularly in the high wavenumber (or frequency) range. This difference is discussed as an 'aliasing' phenomenon that has also been known in steady turbulence.
当将频谱分析应用于诸如主动脉中发现的非定常湍流时，必须考虑两种类型的非定常性。首先，湍流本身的统计特性随时间变化，因此必须重新考虑频谱密度的定义。其次，湍流速度波动，无论它们是稳定的还是非定常的，都由非定常对流速度携带，这会改变静止观察者所看到的它们的特性。在本研究中，通过将泰勒的“冻结湍流”假设应用于具有非定常对流速度的湍流，讨论了后一种意义上的湍流非定常性。如果假设湍流的“冻结”模式和恒定对流速度，测量得到的频谱可以很容易地转换为波数（空间）谱，通常作为归一化过程中一个微不足道的部分。然而，在非定常湍流的情况下，对流速度不再恒定，传统方法无法使用。本文提出了一种估计非定常湍流空间特性的新方法，该方法基于非定常对流速度，通过非线性变换将湍流速度的时间波动转换为空间波动。然后对变换后的数据进行傅里叶分析，直接得到波数谱。所提出的方法应用于犬升主动脉获得的数据。用所提出的方法计算得到的谱与用传统方法得到的谱有显著差异，特别是在高波数（或频率）范围内。这种差异被作为一种在稳定湍流中也已知的“混叠”现象进行了讨论。
