Hill’s vortex is a three-dimensional vortex structure form-preserving solution of the Euler equations (Hill in Philos Trans R Soc Lond A 185:213–245, 1894). For small amplitude axisymmetric disturbances on the external surface, the linear stability analysis by Moffat and Moore (J Fluid Mech 87:749–760, 1978) predicted the formation of a tail. Successive linear and nonlinear investigations confirmed this fact and in addition observed that the shape of the tail was linked to number of small amplitude azimuthal disturbances of the surface. In this paper, the Navier–Stokes equations are solved, at high Reynolds number, by imposing large amplitude axisymmetric and three-dimensional disturbances on the surface of the vortex. The axisymmetric disturbances are convected in the rear side, are dumped and form an axisymmetric wave increasing at the same rate as that in the linear stability analysis. The azimuthal disturbances produce a hierarchy of structures inside the vortex, and in a short-time evolution, the shape of the vortex is maintained. For a long-time evolution, direct numerical simulations show that Hill’s vortex for azimuthal disturbances loses its original form for the formation of a wide range of energy containing scales characteristic of three-dimensional flows. Although a true turbulent state has not been reached, the DNS of this simple vortex structure shows the passage from a vortex dominated to a turbulent state.

希尔的涡旋是Euler方程的三维涡旋结构保形解（Hill in Philos Trans R Soc Lond A 185：213–245，1894年）。对于外表面上的小振幅轴对称扰动，Moffat和Moore的线性稳定性分析（J Fluid Mech 87：749-760，1978）预测了尾巴的形成。连续的线性和非线性研究证实了这一事实，此外还观察到尾巴的形状与表面的小幅度方位角扰动有关。在本文中，通过在涡旋表面施加大振幅轴对称和三维扰动，在高雷诺数下求解Navier-Stokes方程。轴对称扰动在后侧对流，抛弃并形成轴对称波，其增加速度与线性稳定性分析中的增加速度相同。方位角扰动在涡旋内部产生了层次结构，并且在短时的演化过程中，涡旋的形状得以保持。对于长期的演化，直接数值模拟表明，希尔兹的方位角扰动涡流失去了其原始形式，从而形成了具有广泛范围的三维流特征的能量尺度。尽管尚未达到真正的湍流状态，但此简单涡旋结构的DNS显示了从占主导地位的涡旋到湍流状态的通道。对于长期的演化，直接数值模拟表明，希尔兹的方位角扰动涡流失去了其原始形式，从而形成了具有广泛范围的三维流特征的能量尺度。尽管尚未达到真正的湍流状态，但此简单涡旋结构的DNS显示出从占主导地位的涡旋到湍流状态的通道。对于长时间的演化，直接数值模拟表明，希尔的方位角扰动涡流失去了其原始形式，从而形成了具有广泛范围的三维流特征的能量尺度。尽管尚未达到真正的湍流状态，但此简单涡旋结构的DNS显示出从占主导地位的涡旋到湍流状态的通道。