应用谱理论研究压力脉动的湍流模式

本文应用谱分析理论研究了剪切湍流场中的压力脉动,包括功率谱、均方值等.通过对压力脉动Possion方程的Fourier变换,首先将压力脉动谱表示成速度脉动谱的形式.利用Navier-Stokes方程的形式解及准正态分布假设,可以进一步将压力脉动功率谱表达式中所包含的速度脉动的三阶相关与四阶相关表示成速度脉动的二阶相关（功率谱）.最后,引入高雷诺数流的速度脉动功率谱模型,导出了由湍动e₀,耗散ε,雷诺应力-iu_j>及时均速度梯度表示的压力脉动均方值的湍流模式,并同现有数据进行了比较.

Investigation of the Turbulent Model for Pressure Fluctuations with Spectral Theory

The pressure fluctuations in turbulent shear flows are investigated with the theory of spectral analysis. An expression for pressure spactra is analytically derived in terms of velocity spectra. This derivation is based on a formal solution of the Navier-Stokes equation and quasi-normal assumption to express the third and fourth order velocity correlations in terms of double velocity correlation. Then, a turbulent model for the commutation of pressure fluctuation intensity with Renolds stress and mean flow velocity gradients is established.The turbulent constants in the model are calculated from the assumptions about the general behaviour of velocity spectra in high Renolds number flows, Comparison with direct simulation of turbulent boundary layer is made. It is found that the turbulent-turbulent, cross correlation, and turbulent-shear source terms for mean-square value of pressure fluctuation are about the same magnitude.