A local analysis of the axi-symmetric Navier-Stokes flow near a saddle point and no-slip flat boundary
This work provides numerical insights into the dynamics of swirling flows near boundaries, which is relevant for understanding tornado behavior, but the results are incremental and specific to the simulated configuration.
The paper numerically simulates axi-symmetric Navier-Stokes flows with a no-slip flat boundary to study swirling structures in tornado-like flows. It finds that with swirl, the distance from the maximum velocity point to the axis changes drastically at a turning point, and an increasing velocity phenomenon occurs near the boundary and axis.
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.