中文摘要：

基于泛函分析中的不动点理论,采用不动点方法首次获得混合层无粘线性稳定性方程的显式Legendre级数解,该级数解在整个无界流动区域内一致有效.现有基于传统摄动法得到的无界流动区域一致有效解仅适用于长波扰动和中性扰动两种特殊情况,而使用不动点方法可以得到所有不稳定扰动波数的特征解.另外,在不动点方法框架下,扰动相速度和扰动增长率可根据方程的可解性条件来唯一确定.为了验证该方法的有效性,将该方法和现有文献中的数值计算结果相比较,结果表明该方法具有精度高、收敛快等优点.

英文摘要：

Based on the fixed point concept in functional analysis,the fixed point method（FPM） was used to analyze the invisicd stability equation of the mixing layer,and an explicit semi-analytical solution in Legendre series form was obtained.It is different from other existing analytical methods,such as the well-known perturbation technique,because FPM can obtain a uniformly convergent solution in the full infinite flow domain.Meanwhile,the present Legendre series solution is valid to all wave numbers.What＇s more,in the framework of FPM,the eigenvalue can be determined by the solvability condition in a straightforward manner.Finally,the comparison between FPM and other numerical methods shows that FPM is of high accuracy and efficiency.