论文标题
三维的不稳定性和山丘涡流的破坏
The three-dimensional instabilities and destruction of the Hill's vortex
论文作者
论文摘要
山涡流是Euler方程的三维涡流结构解决方案。对于通过\ citet {Moff78}进行线性稳定性分析的外表面上的小振幅轴对称干扰，出现了尾巴的形成。连续的研究证实了这一事实，此外，观察到具有方位角小振幅干扰的尾巴形状不同。在本文中，在雷诺数的高值下求解了Navier-Stokes方程，在涡流表面施加了大幅度轴对称和三维干扰。结论是方位角干扰产生了涡流内部结构的层次结构，以保持涡流的形状。另一方面，轴对称干扰在后侧被倾倒，形成轴对称波的时间更长，比表面干扰的大小更高。移动框架中的模拟可以扩展时间的演变，从而得出这样的结论：山涡流是不稳定的，并产生了包含三维流量的尺度特征的广泛能量。
The Hill vortex is a three-dimensional vortex structure solution of the Euler equations. For small amplitude axisymmetric disturbances on the external surface from the linear stability analysis by \citet{moff78} emerged the formation of a tail. Successive studies confirmed this fact, and in addition observed a different shape of the tail with azimuthal small amplitude disturbances. In this paper the Navier-Stokes equations are solved at high values of the Reynolds number imposing large amplitude axisymmetric and three-dimensional disturbances on the surface of the vortex. The conclusion is that the azimuthal disturbances produce a hierarchy of structures inside the vortex maintaining the shape of the vortex. On the other hand the axisymmetric disturbances are convected in the rear side, are dumped and form an axisymmetric wave longer higher the magnitude of the surface disturbance. Simulations in a moving frame allow to extend the evolution in time leading to the conclusion that the Hill vortex is unstable and produces a wide range of energy containing scales characteristic of three-dimensional flows.
