  As one of the violent flow, tornadoes occur in many place of the world. In
order to reduce human losses and material damage caused by tornadoes, there are
many research methods. One of the effective methods is numerical simulations
such as the work in a recent article Ishihara et al. (2011). The swirling
structure is significant both in mathematical analysis and the numerical
simulations of tornado. In this paper, we try to clarify the swirling
structure. More precisely, we do numerical computations on axi-symmetric
Navier-Stokes flows with no-slip flat boundary. We compare a hyperbolic flow
with swirl and one without swirl and observe that the following phenomenons
occur only in the swirl case:
  The distance between the point providing the maximum velocity magnitude |v|
and the z-axis is drastically changing around some time (which we call it
turning point). An "increasing velocity phenomenon" occurs near the boundary
and the maximum value of |v| is obtained near the axis of symmetry and the
boundary when time is close to the turning point.
