Summary A class of axisymmetric vortex solutions superposed upon radial stagnation flows is described. The new vortex solutions generalize the classical Burgers’ vortex and Sullivan’s vortex solutions in the presence of a volumetric line source at the symmetry axis, the former approaching the Burgers’ vortex sheet when the source strength becomes very large. The stability of the generalized Burgers’ vortex is studied. In a different manner from the classical solution, the generalized Burgers’ vortices are found to be unstable for two-dimensional disturbances when the vortex Reynolds number is increased above a critical value, for a fixed strength of the volumetric source.

中文翻译：

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径向停滞流中的稳定轴对称涡旋

总结 描述了叠加在径向停滞流上的一类轴对称涡旋解。新的涡旋解在对称轴存在体积线源的情况下推广了经典的 Burgers 涡和 Sullivan 涡解，当源强度变得非常大时，前者接近 Burgers 涡片。研究了广义Burgers涡旋的稳定性。与经典解决方案不同的是，当体积源的固定强度时，当涡流雷诺数增加到临界值以上时，广义 Burgers 涡流对于二维扰动是不稳定的。