中文摘要：

建立了一个基于Fourier方法的悬停状态旋翼尾迹稳定性分析方法，在此基础上，推导给出了旋翼尾迹涡线上的任意扰动量被离散成一组Fourier级数时，各阶谐波波长的取值范围，从而进一步完善了旋翼尾迹稳定性分析方法的理论依据；并提出一种利用发散率上下界来进行尾迹涡线稳定性分析的方法，用以分析在不同旋翼参数下稳定特性沿尾迹寿命角的分布特性，从而将原来针对单一节点的稳定性分析拓展至整根旋翼尾迹的全局稳定性分析中。以悬停状态下的H-34型直升机旋翼为算例，使用该方法着重计算分析了尾迹根数（桨叶片数）、涡核分布、尾迹畸变等主要因素对旋翼尾迹稳定性的影响。分析结果表明：就局部而言，旋翼尾迹上单一节点都是本质不稳定的，而在全局上，其不稳定性沿尾迹涡线寿命角的整体分布会受多种因素影响，并呈现出有规律的变化特性。进一步，通过与悬停状态下旋翼尾迹非周期性试验结果的对比，表明该方法能够有效地模拟扰动量沿旋翼尾迹的发散特性。

英文摘要：

A method of rotor wake stability analysis in hovering state by Fourier method is established. By the present method, the interval of harmonic wavelength is given when any disturbance on the rotor wake is separated into Fourier series, by which the theoretical foundation of rotor wake stability analysis is im- proved. Furthermore, a methodology, which can extend the stability analysis for single collocation point to the whole rotor wake by extracting and analyzing the upper and lower bound of the divergence rate relative to the vortex age, has been presented. Taking the rotor of H-34 helicopter in hovering state as a numerical ex- ample, the influence of the number of wakes （blades）, distribution of vortex core and distortion of wake on rotor wake stability is investigated by this method. The results show that, as for a single collocation point on the rotor wake, it is intrinsically unstable, while as for the whole rotor wake, its stability relative to the vor- tex age is affected by many factors and exhibits some variation characteristics. Moreover, by comparing with the experimental data of aperiodicity of the hovering rotor wake, it is proved that this method can effectively predict the growth characteristics of any disturbance on the rotor wake.