However, if instead of only points, we pick an entire region on this sphere, as you can see the north and south pole regions here, we obtain vortex tubes.

不过，如果我们不是单挑点，而是选择球体上一整片区域，你就能看到，我们在南北极这里获得了涡管。

These vortex tubes provide an accurate representation of the vorticity information within the simulation, and this is one of the rare cases where the validity of such a solution can also be shown.

在模拟中，这些涡管实现了旋涡信息的一个精确再现，这是展现这样一个解法的精确度中一个罕见的实例。