The effects of different axisymmetric forebody shapes have been studied on the non-axisymmetric (helical) global modes of the boundary layer developed on a circular cylinder. Sharp cone, ellipsoid and paraboloid shapes have been considered with the fineness ratio (FR) of 2.5, 5.0 and 7.5. The base flow is in line with the cylinder’s axis at the inflow boundary, and hence the base flow is axisymmetric. The boundary layer has developed from the tip of the forebody where a highly favourable pressure gradient exists, and it depends on the sharp edge of the forebody’s geometric shape. However, the pressure gradient then remains constant on the cylindrical surface of the main body. Thus, the boundary layer developed on the forebody and main body (cylinder) is non-parallel, non-similar and axisymmetric. The governing equations for the stability analysis of the small disturbances have been derived in the cylindrical polar coordinates. The spectral collocation method with Chebyshev polynomials has been used to discretise the stability equations. An eigenvalue problem has been formulated from the discretised stability equations along with the appropriate boundary conditions. The numerical solution of the eigenvalue problem was done using Arnoldi’s iterative algorithm. The global temporal modes have been computed for helical modes \(N = 1\), 2, 3, 4 and 5 for Reynolds number \(Re = 2000\), 4000 and 10000. The spatial and temporal structures of the least stable global modes have been studied for different Reynolds numbers and helical modes. The global modes with ellipsoid were found the least stable while that of the sharp cone were found the most stable.

已经研究了不同轴对称前体形状对在圆柱上形成的边界层的非轴对称（螺旋）全局模式的影响。细度比 (FR) 为 2.5、5.0 和 7.5 时考虑了尖锥、椭圆体和抛物面形状。基流在流入边界处与圆柱的轴线一致，因此基流是轴对称的。边界层是从前体尖端发展而来的，那里存在非常有利的压力梯度，它取决于前体几何形状的锐利边缘。然而，压力梯度在主体的圆柱表面上保持恒定。因此，在前体和主体（圆柱体）上发育的边界层是非平行、非相似和轴对称的。小扰动稳定性分析的控制方程已经在圆柱极坐标中推导出来。Chebyshev 多项式的谱配置方法已被用于离散稳定性方程。一个特征值问题已经从离散的稳定性方程连同适当的边界条件一起被公式化了。特征值问题的数值解是使用 Arnoldi 的迭代算法完成的。已为螺旋模式计算了全局时间模式 特征值问题的数值解是使用 Arnoldi 的迭代算法完成的。已为螺旋模式计算了全局时间模式 特征值问题的数值解是使用 Arnoldi 的迭代算法完成的。已为螺旋模式计算了全局时间模式\(N = 1\) , 2, 3, 4 and 5 for Reynolds number \(Re = 2000\) , 4000 and 10000. 研究了不同雷诺数和螺旋的最不稳定全局模式的空间和时间结构模式。发现具有椭圆体的全局模式最不稳定，而发现尖锐圆锥体的全局模式最稳定。